ARCHIVE: 2011
December 28, 2011– 3

It’s been an exciting year for us here at Wolfram|Alpha, and we wanted to say thank you to all of our loyal blog readers. We thought we would take a look back at 2011 by sharing some of this year’s most popular Wolfram|Alpha Blog posts. This year we saw some exciting content additions, brand-new ways of accessing and interacting with Wolfram|Alpha, and an arsenal of apps for students and professionals alike.

Each of these are only highlights of the blog posts of 2011. For a little extra reading, you can visit the 2011 archive to see all of the blog posts from this year. More »

December 19, 2011– 5

We are pleased to add our latest work in the domain of radiation shielding to our ever-widening repertoire of highly technical and challenging areas. Although this was one of the earliest features added to Wolfram|Alpha, we have now significantly expanded the functionality of the area that permits users to ask about the shielding efficacy of numerous materials against multiple radiation sources. Most importantly, we have now included the computations for shielding against that most dreaded radiation—the gamma ray. We think these new features will be extremely useful in helping people to better understand the common shielding gadgets they might see every day (such as at the dentist’s office or when getting an X-ray).

At launch we had information only for beta radiation (electron beam) but now have added alpha particles, protons as well as photons to our collection. Additionally, we have significantly improved the natural-language capabilities in this domain. For example, asking Wolfram|Alpha “At what thickness of lead is 3 MeV gamma radiation halved in intensity?” immediately returns the thickness of the lead sheet as the result. Or maybe you’re interested in figuring out how far alpha particles travel through air. Just ask, “What thickness of air will shield 5 MeV alpha particle radiation?” What if there is a glass window? Once again, the query is at your fingertips: “What is the maximum electron radiation that a 2″ thick plate glass can block?More »

December 15, 2011– 12

Just in time for the holidays, we’re introducing a new functionality that provides consumers with a unique approach to shopping. By leveraging data from Best Buy’s public APIs, Wolfram|Alpha users will now be able to browse more than 35,000 appliances and consumer electronics products. Wolfram|Alpha’s intuitive natural-language interface helps you hone in on the precise products you need, while its powerful data visualization capabilities give you an innovative overview of any shopping category.

We’ve taken the strengths we’ve developed in math, science, and socioeconomic data and created something equally unique and useful for online shoppers. Type in the name of a product category—”dishwashers” or “tablet computers,” for example—and Wolfram|Alpha generates a comprehensive, custom analysis. What are the typical dimensions and other physical characteristics of other products in this class? How common is a given product feature? Wolfram|Alpha helps you to answer these questions.

Type in a specific product name or model number—say, “Samsung GT-P3113TSYXAR”—and Wolfram|Alpha will highlight that product’s rank within the entire product category. From a glance at the plots below, you can see that this tablet falls pretty squarely in the middle of the pack with regard to price and generally on the low-end to average range for a variety of physical and performance attributes.

Samsung GT-P3113TSYXAR More »

December 13, 2011– 8

Today we are happy to add a new addition to our line of Course Assistants for iOS: the Wolfram Mechanics of Materials Course Assistant. The app was created specifically to aid those taking their first mechanics of materials class.

Wolfram Mechanics of Materials Course Assistant More »

December 12, 2011– 2

The hyperlink has been one of the most powerful tools of the information age. Links make it easier to navigate the complex web of information online by combining the information itself with the method for retrieving it. Clicking a link means “tell me more about this thing,” which naturally lends itself to “surfing.”

At Wolfram|Alpha, we strive to integrate and leverage technologies to create the most powerful computational capabilities and user experiences possible. In Wolfram|Alpha, the output comes in the form of a “report.” If you want to know more about something in the output of an Wolfram|Alpha query, clicking it as a link will generate another such report. Though we’ve had links in Wolfram|Alpha for a while, we’ve recently taken them to the next (computable) level: Wolfram|Alpha now computes links dynamically based on the output generated by your query.

Clicking a link basically feeds the plaintext of that link back into Wolfram|Alpha, creating new output with new links. Thus the navigational ability of the world wide web and the computational ability of Wolfram|Alpha are now intertwined and can feed off each other. You can now surf Wolfram|Alpha like you can surf the Internet. More »

December 9, 2011– 0

Wolfram Fractals Reference App

Making your list and checking it twice, but still don’t know what to get for the last few people on your list? Gift a Wolfram app! From now through December 31, select apps are 50% off. We have apps for snowbirds and travelers, students and teachers, history buffs, word game enthusiasts, casino lovers, lawyers, network administrators, and lifelong learners—everyone, really! More »

December 6, 2011– 7

We are happy to announce our second Professional Assistant App for iOS: the Wolfram Lawyer’s Professional Assistant. This innovative app utilizes the power of Wolfram|Alpha to provide detailed reference information and data for legal professionals on the go.

Wolfram Lawyer's Professional Assistant More »

December 5, 2011– 3

In his classic sci-fi television series Star Trek, Gene Roddenberry dreamt of a computer that could help its user with pretty much anything. Ask it a question; it has an answer. Need some Earl Grey tea? It can materialize it for you. Need to create a self-aware, artificially intelligent program based on a Sherlock Holmes character in order to defeat Data? Easy. While we can’t materialize anything for you or create a self-aware, artificially intelligent program, we are on track to make all the world’s knowledge computable, with the hopes of someday answering all of your factual questions. In some cases, we are doing a bit better than the Star Trek computer:

More »

November 29, 2011– 7

Permutations are among the most basic elements of discrete mathematics. They are used to represent discrete groups of transformations, and in particular play a key role in group theory, the mathematical study of symmetry. Permutations and groups are important in many aspects of life. We all live on a giant sphere (the Earth) whose rotations are described by the group SO(3) (the special orthogonal group in 3 dimensions). On the micro-scale, the Hungarian-American physicist Eugene Wigner (November 17, 1902–January 1, 1995), who received a share of the Nobel Prize in Physics in 1963, discovered the “electron permutation group”, one of many applications of permutation groups to quantum mechanics.

Permutations deserve a full treatment in Wolfram|Alpha. Since Mathematica 8 provides new functionality to work with permutations using both list and cyclic representations, we now have a powerful new way of working with permutations using natural language.

Let’s first define permutations, then discuss how to work with them in Wolfram|Alpha. A permutation of a set X is a bijective (one-to-one and onto) mapping of X to itself. There is a convenient way of specifying a permutation α of a finite set of n elements: write down the numbers 1, 2, …, n in a row and write down their images under α in a row beneath:

Example of a permutation More »

November 22, 2011– 6

Last week we showed you some of the ways Wolfram|Alpha can display flight information. Now you can take that functionality with you wherever you go with the Wolfram Flight Information Reference App for iOS.

Flight Information Reference App More »

November 21, 2011– 10

Creating strong passwords is an important part of online security. Now it is even easier to create strong passwords and check the strength of existing passwords with the Wolfram Password Generator Reference App for iOS.

Wolfram Password Generator Reference App More »

November 17, 2011– 25

At one time or another, we’ve all looked at a jet flying high overhead and thought “I wonder where they’re headed?” Actually answering that question probably seemed impossible before—but if you’re a user in the United States, Wolfram|Alpha can now help you answer that question and many more interesting queries about commercial and other flights.

Try the simple query “flights overhead” and you’ll get information on aircraft that should be visible to you, assuming a clear sky and unobstructed view. If you’re on a location-aware mobile device, the results should be based on your precise latitude and longitude—otherwise, Wolfram|Alpha will use the best available location information from your browser. Also note that hovering over an individual plane in the sky map will produce a tooltip with the airline and flight number:

flights overhead More »

November 16, 2011– 3

Helping educators utilize Wolfram|Alpha in the classroom to enhance their lessons is one of our missions, and we love to learn about the creative ways teachers use Wolfram|Alpha.

One such example is Matt Arnold, a STEM (science, technology, engineering, and mathematics) teacher at Skiles Test Elementary in Indianapolis who started a Wolfram Math Club. The club consists of seven sixth-graders who meet twice a week to complete projects utilizing Wolfram|Alpha.

Wolfram Math Club More »

November 10, 2011– 7

We are happy to announce that we released two new entries into our line of Wolfram|Alpha-powered iOS apps: the Wolfram Investment Calculator Reference App and the Wolfram Gaming Odds Reference App. The Wolfram Investment Calculator Reference App was built specifically to help users get the most from their investments, and the Wolfram Gaming Odds Reference App provides the probabilities and odds of winning many popular card and lottery games.

Wolfram Investment Calculator Reference App Wolfram Gaming Odds Reference App More »

November 4, 2011– 1

This Sunday, over 40,000 runners will take part in the New York City Marathon. A great amount of preparation and planning goes into accommodating such a large group of athletes, as well as the fans cheering on the sidelines. An article in The New York Times described the numbers behind planning such a huge race, so we decided to plug those numbers into Wolfram|Alpha and see what interesting things we could compute.

According to the article, over 43,000 athletes took part in the 26.2-mile race last year. Typing “running 26.2 miles” into Wolfram|Alpha allows you to enter your pace, gender, and body weight, then receive data based on your inputs, such as calories burned and oxygen consumed.

running 26.2 miles More »

October 28, 2011– 1

With Halloween around the corner, everyone’s thinking about costumes, trick-or-treating, and jack-o’-lantern carving and figuring out what to do with a 1,818 pound pumpkin. While the latter might only be true for the owners of this year’s largest pumpkin, Wolfram|Alpha has something for everyone this Halloween. The nearly one-ton squash belongs to a farmer from Quebec, Canada. Besides carving it into a giant jack-o’-lantern, the next best thing to do with that much pumpkin is make enough pumpkin pie for a small town. A common recipe for a pumpkin pie calls for two cups of pumpkin. Using Wolfram|Alpha, we find that 1,818 pounds of pumpkin will allow us to make 3,550 pumpkin pies.

Hopefully you are in a giving mood, so you can cut each pie into eight slices to come up with just enough to share with the entire town of Allen Park, Michigan. With 28,210 people in Allen Park and 28,400 slices of pie, you’re still left with 190 slices to put in the freezer for later. More »

October 25, 2011– 0

The United Nations (UN) was officially founded 66 years ago this week, bringing together “peace-loving states” (as the Charter of the UN described them) to cooperate on issues of international law, economic and social development, human rights, and other matters of critical importance to global human development. From the time it launched, Wolfram|Alpha has relied on a wide variety of datasets provided by various UN organizations—and as recent blog posts indicate, these agencies remain an important source of information for international data. More »

October 21, 2011– 4

We’ve blogged before about Wolfram|Alpha’s powerful relocation calculator, which has turned out to be one of our more popular—and practical—features. Our last round of enhancements added information about broad topics like population, home sale prices, unemployment rates, and more; now we’ve added more detail to the core cost-of-living categories, so you can see how prices of specific retail goods and services differ among US cities and metropolitan areas. More »

October 18, 2011– 3

We’ve blogged before about international food consumption data in Wolfram|Alpha, and queries about this data have proved to be a favorite among our users, with good reason: it’s fascinating to explore the world’s food supply and to visualize trends in consumption. In an attempt to fill in a more complete picture of global agricultural trends, we’ve added more data from the FAO—this time covering food production, harvest, and crop yields around the world. More »

October 13, 2011– 0

We here at Wolfram|Alpha are constantly trying to improve the user experience by fine-tuning our algorithms and making our functionality in every domain more versatile and flexible. We are pleased to announce that we have made useful upgrades to chemistry functionality in Wolfram|Alpha, especially in the domain of solution chemistry. We have new data that enables you to quickly determine whether a given set of solvents are miscible in each other or not: “Is acetone miscible in benzene?” You also could ask for the list of liquids that are miscible in a given solvent: “What solvents are miscible in acetone?” We are improving our coverage of this area, with new data being added regularly.

What solvents are miscible in acetone More »

October 6, 2011– 23

I’m so sad this evening—as millions are—to hear of Steve Jobs’s death. Scattered over the last quarter century, I learned much from Steve Jobs, and was proud to consider him a friend. And indeed, he contributed in various ways to all three of my major life projects so far: Mathematica, A New Kind of Science and Wolfram|Alpha.
More »

October 3, 2011– 7

As most Wolfram|Alpha blog readers know, the engine behind the Wolfram|Alpha computational knowledge engine is Wolfram Research’s powerful mathematics and computation software, Mathematica. Ironically, while Wolfram|Alpha contains thousands of datasets on diverse and sundry subject areas, until very recently, its computable knowledge of the Mathematica language itself has been somewhat limited. More »

September 30, 2011– 5

Wolfram Course Assistant Apps for iOS
If you missed out on our previous Wolfram Course Assistant Apps sale, you are in luck this weekend. Through this Sunday, October 2, you can save up to 50% in the iTunes App Store on all the Wolfram Course Assistant Apps.

Pre-Algebra, Calculus, Physics, Statistics, Music Theory, Astronomy, and many more powerful apps are ready to help you in the classroom! More »

September 28, 2011– 1

Diving organizations such as PADI® or NAUI provide certified recreational scuba divers with a dive table to determine how long a diver can stay underwater at a given depth, both for the initial and subsequent dives. The reason for the dive planner is to ensure that the amount of nitrogen your body absorbs during a dive remains within acceptable limits.

Dive tables do not tell you how much nitrogen has accumulated in your body after a dive; they simply tell you how long you can stay at a given depth without having to have a mandatory decompression stop.

Recreational dive tables come in the form of a plastic coated card, and for many recreational divers these cards are daunting and look very complicated. For example, the PADI® dive card has tables on both sides of the card, containing over a thousand numbers.

At Wolfram|Alpha we have removed the complexity of trying to read the NAUI and PADI® dive tables.

Recreational dive planner More »

September 27, 2011– 3

We are happy to announce that today we are releasing two more Wolfram|Alpha-powered Reference Apps for iOS: the Wolfram Mortgage Calculator Reference App and the Wolfram Words Reference App.

Wolfram Mortgage Calculator Reference AppWolfram Words Reference App
More »

September 20, 2011– 2

Thank you to everybody who submitted a photo as part of our Big Spikey on Campus Contest! We loved seeing all of the creative ways Spikey was used on campuses around the world. It was a tough decision, but we’ve finally chosen the best submissions. Each of the winners will be contacted through Twitter or Tumblr. More »

September 16, 2011– 2

Wolfram Course Assistant Apps for iOS

Today we’ve got exciting news for students everywhere—Wolfram Course Assistant Apps are on sale in the iTunes store through this Sunday, September 18. You can save up to 50%! Physics, Calculus, Algebra, and many more powerful apps are ready to help you excel this semester. Consider this a back-to-school gift from Wolfram|Alpha! More »

September 13, 2011– 1

Learning all about the 50 US states and the history of the presidents of the United States is a pivotal part of the education of Americans. To assist people learning about these key aspects or those who want to freshen up on their trivia, we have released the Wolfram US States Reference App and the Wolfram US Presidents Reference App, both for iOS.

Wolfram US Presidents Reference AppWolfram US States Reference App
More »

September 8, 2011– 3

Earlier this year, we added data on all 18,000+ US public school districts to Wolfram|Alpha, allowing you to analyze student and teacher populations and detailed revenue and expenditure data for individual districts or across all the districts in a given city or county. We had a terrific response to this—lots of people wrote in to tell us they learned some useful information about their own districts and others across the country. And virtually all of those people ended their messages with “But when will you have information about individual schools?”

We’re happy to announce that Wolfram|Alpha now has data on nearly 108,000 public schools in the United States, which is based on 2009-10 school year data from the National Center for Education Statistics (NCES). So if you go back and try the first input from our earlier post on school districts, you’ll notice that the result looks quite different—the result for “Seattle public schools” now defaults to a summary of data on individual schools rather than the district itself (which is still available by clicking “Use the input as a US school district instead”).

Seattle public schools More »

September 7, 2011– 4

We’ve highlighted data from the World Bank’s World Development Indicators (WDI) database in previous blog posts about employment and business statistics. As many of our users head back to school, it seems like the right time to show off some additional World Bank statistics about education. Wolfram|Alpha can now answer a broad range of simple questions about student and teacher populations in various countries, such as:

You can also ask questions about student performance and progression in a given country or between multiple countries:

More »

September 6, 2011– 12

It’s back to school time again, and we here at Wolfram|Alpha know that a new school year can be expensive for both students and parents. Books, clothes, food, computers—it can all add up. That is why we’re giving away free stuff! Over the next two weeks, we will be giving away Wolfram|Alpha merchandise, such as T-shirts, mugs, and our apps, through our Twitter account. In addition to the two weeks of daily giveaways, there is also a chance to win an iPad 2 filled with our apps by participating in the Big Spikey on Campus Contest.

Big Spikey on Campus
More »

September 1, 2011– 3

While mathematics and music are inextricably linked, music is often regarded as magical. It transcends emotion and nature in a way that is often hard, if not impossible, to properly explain. For example, many people are deeply affected by the emotional power of Beethoven’s Ninth Symphony, but may not fully understand why. Perhaps great composers simply intuit mathematical connections to music.

But even music has plenty of structures that are clearly identifiable and thus computable. At Wolfram|Alpha, we are working hard to identify these underlying structures and are coming up with exciting ways to bring them to life.

Take a musical scale as an example. While we are used to arpeggios and melodic figures fluttering through familiar musical pieces, it is helpful to see that at its core, a scale has an intrinsic structure. Each pitch relates to the next by a certain measurable difference. Further, each of the pitches, which we perceive generally as high or low in a pitch space, has a specific frequency. More »

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August 30, 2011– 12

Things with Wolfram|Alpha are going well. Really well. So well that I’m now incredibly keen to scale them up dramatically.

When I started the Wolfram|Alpha project, I was not even sure anything like it would be possible. But over the last two years we’ve proved that, yes, with the tower of technology we’ve created, one can in fact take large swaths of knowledge, make them computable, and deliver them for everyone to use.

From the outside, it’s easy to see that there’s been steady growth in the domains of knowledge that Wolfram|Alpha covers. And over the next few months there’ll be some big additions, notably in everyday and consumer areas. But to me what’s most dramatic is what’s happened on the inside. Because what we’ve done is to build a giant system of technology and management processes that allows us systematically to make any area of knowledge computable.

The catch is that it always takes effort. We rely on a huge tower of automation. But in every new area we tackle there are new issues, new opportunities—and new ways that resources and human effort have to be used.

I’m very pleased with how broad and deep the coverage we have already achieved is. But we have an immense to-do list, assembled not least from all the feedback we’ve received from users of Wolfram|Alpha. And the good news is that at this point it’s a straight shot: given enough effort, we can complete the to-do list. We have all the systems we need to scale the knowledge in Wolfram|Alpha up all the way. More »

August 25, 2011– 0

One fall evening in 1843, a man walked past the Brougham Bridge along the Royal Canal in Dublin, Ireland. Suddenly, he felt a flash of insight so strong he was compelled to etch his thoughts into the rock on the side of the bridge. This is what he wrote:

i2 = j2 = k2 = i j k = -1

The man was mathematician William Rowan Hamilton, and the insight was of a number system that could represent forces and motions in three-dimensional space. Hamilton called his numbers “quaternions”, because each has four parts: a real number part, and three other parts labeled with i, j, and k, each of which is also a real number. For example, 2 + 3i + 0.342j – 2k is a quaternion. More »

August 22, 2011– 2

Wolfram|Alpha goes back to school

Is it really possible that yet another summer is drawing to a close? Here at Wolfram|Alpha, we’ve spent our summer getting ready to head back to school—building new course assistant apps, adding new data, and even making Wolfram|Alpha interactive with CDF. As the world’s leading knowledge engine, we’ve made it our mission to continually improve and ensure that we’re helping students and teachers around the globe explore concepts, ideas, and calculations on a deeper level than previously possible. More »

August 17, 2011– 18

Back in June we released the Wolfram Physics I Course Assistant to aid those taking introductory physics classes. We are now releasing the Wolfram Physics II Course Assistant for iOS to help those continuing their physics education.

Wolfram Physics II Course Assistant More »

August 16, 2011– 4

The precursors of what we’re trying to do with computable data in Wolfram|Alpha in many ways stretch back to the very dawn of human history—and in fact their development has been fascinatingly tied to the whole progress of civilization.

Last year we invited the leaders of today’s great data repositories to our Wolfram Data Summit—and as a conversation piece we assembled a timeline of the historical development of systematic data and computable knowledge.

This year, as we approach the Wolfram Data Summit 2011, we’ve taken the comments and suggestions we got, and we’re making available a five-feet-long (1.5 meters) printed poster of the timeline—as well as having the basic content on the web.

Historical data timeline

The story the timeline tells is a fascinating one: of how, in a multitude of steps, our civilization has systematized more and more areas of knowledge—collected the data associated with them, and gradually made them amenable to automation. More »

August 11, 2011– 10

Two weeks ago we made a major announcement: building on technology that we’ve been developing for more than 20 years, we released Computable Document Format (CDF). I think CDF is going to have a big effect on the way all sorts of things can be  communicated. Because for the first time it makes it practical to include live computation as a routine part of a document.

There are many important applications of CDF that we’ll no doubt be seeing over the months and years to come. But today I’m pleased to announce an experimental one from us: Wolfram|Alpha with CDF.

sin(|x|)^|x|

Starting today, as soon as you have the free CDF plugin installed (or if you have Mathematica 8 on your system) you can go to the top right-hand corner of the Wolfram|Alpha website, and set CDF on, with the result that Wolfram|Alpha will generate not just a static web page, but instead full CDF output—that you can directly interact and compute with. More »

August 10, 2011– 0

Recently we released our pregnancy data content, accessible through various queries such as “pregnant 18 weeks” or “pregnant, fetus’s weight 5 lbs 4 oz”. To add to that data, we have created an Apgar score calculator and assessment tool.

The Apgar score is a value assigned to newborn babies within the first 5 to 10 minutes of life. This value is a quick assessment of the baby’s overall health based on 5 variables: the color of the baby’s body and extremities, pulse, reaction (e.g., facial expression, cry response) to stimulation of the nose or feet, muscle tension after stimulation, and respiratory activity. All of these variables can be described more simply as appearance, pulse, grimace, activity, and respiration. Not so coincidentally, the first letters of these descriptions form an acronym that corresponds to the physician who developed the scale, Dr. Virginia Apgar. More »

August 8, 2011– 16

Today we are releasing our Wolfram Pre-Algebra Course Assistant App for iOS, expanding our planned series of Course Assistant Apps built using Wolfram|Alpha technology.

Wolfram Pre-Algebra Course Assistant
More »

August 5, 2011– 2

Game theory is a rich branch of mathematics that deals with the analysis of games, where, mathematically speaking, a “game” can be defined as a conflict involving gains and losses between two or more opponents who follow formal rules.

Mathematical games can be very simple, such as the game of chicken (which is not recommended in practice):

Chicken game More »

August 4, 2011– 9

Planning a trip can be exhausting, but we believe that everything becomes easier with a little data! Today we released the Wolfram Travel Assistant App, another in our line of Wolfram|Alpha-powered iOS apps. Whether you need help during trip planning or while currently on a vacation, this app is a great addition to your itinerary!

Wolfram Travel Assistant App
More »

August 3, 2011– 1

In my last blog post on plotting functionality in Wolfram|Alpha, we looked at 2D and 3D Cartesian plotting. In this post, we will look at 2D polar and parametric plotting.

For those of you unfamiliar with polar plots, a point on a plane in polar coordinates is located by determining an angle θ and a radius r. For example, the Cartesian point (x, y) = (1, 1) has the polar coordinates (r, θ) = (√2,π/4). The following diagram illustrates the relationship between Cartesian and polar plots.

Relationship between Cartesian and polar plots

To generate a polar plot, we need to specify a function that, given an angle θ, returns a radius r that is a function r(θ). Making a polar plot in Wolfram|Alpha is very easy; for example, we can plot Archimedes’ spiral. More »

August 2, 2011– 10

It seems the sun won’t let up this summer, with many parts of the United States experiencing record-level temperatures. With the excessive heat comes the danger of overexposure to the sun, but it’s often hard to know you’re at risk until it’s too late. The newly released Wolfram Sun Exposure Reference App for iOS can aid in calculating just how much sun is too much and can offer recommendations on which SPF level to apply.

Wolfram Sun Exposure Reference App
More »

July 27, 2011– 7

In recent dinner conversation with my brother, I commented that I was “99.9 repeating” percent sure that my favorite author, Jorge Luis Borges, had lived into the 1980s (Wolfram|Alpha later showed me that he did, in fact, live through 1986!). I felt confident about my knowledge, but wanted to leave myself a little wiggle room, just in case. My brother grinned at me and said, “I know you know your geometric sequences. If you say you’re 99.9 repeating percent sure, then you’re 100 percent sure.”

I blushed, embarrassed. He was definitely right!

But just what did my brother mean? Well, he reminded me that:

99.999… = 99 + 9/10 + 9/100 + 9/1000 + 9/10000…

Glancing at the above, the series 9/10 + 9/100 + 9/1000 + 9/10000… stands out. Each term in this series is 1/10 times the term before it, making it a geometric series. A geometric series is a series wherein each term in the sequence is a constant number, r, multiplied by the term before it. Any geometric series whose r satisfies -1 < r < 1 is a convergent series, and we can say to what the series converges:

Sum[r^k, {k, 0, ∞}] = 1/(1-r)

More »

July 19, 2011– 3

Want to know if you and your 20 teammates can march in perfect triangular formation in a parade? Or maybe you want to know how many glasses you’ll need in order to break the world record for largest champagne pyramid (currently 60 stories high, with 37,820 glasses).

Whether you’re stacking watermelons or water-skiers or just playing with dots on paper, if you want to make a perfect geometrical formation, then you’re interested in “figurate” numbers. These are numbers for which that number of things can be arranged into a perfect geometrical shape, such as a triangle (in the case of the “triangular numbers”) or a triangular pyramid (AKA, a tetrahedron), which is the shape of champagne pyramids.

Wolfram|Alpha now has the ability to tell you if a given number is any figurate number. Entering our first question, “Can 21 people be put into a perfect triangle formation?”, into Wolfram|Alpha gives an affirmative, along with a diagram and other useful information:

Can 21 people be put into a perfect triangle formation? More »

July 15, 2011– 2

Periodic tilings (also known as tessellations) are often beautiful arrangements of one or more shapes, known as tiles, into regular patterns, which if extended infinitely are capable of covering the entire plane without gaps. Wolfram|Alpha has possessed detailed knowledge on more than 50 common (and uncommon) varieties of periodic tilings for some time, as illustrated, for example, in the case of the basketstitch tiling:

Periodic tilings possess an individual motif (more formally known as a primitive unit) that is repeated iteratively in a predictable (periodic) way. Such tilings are therefore intimately related to the set of symmetry groups of the plane, known as wallpaper groups. While the most general set of geometric similarity (i.e., shape-preserving) operations in the plane includes rotation (change in angle), dilation/expansion (change in size), reflection (flipping about an axis), and translation (change in position), only translation is needed to produce a periodic tiling from a correctly constructed primitive unit. More »

July 14, 2011– 5

On a moonlit stroll, a young man points to the cloudless sky and says, “Look—a full moon!”

His date is not impressed. “Technically,” she replies, “the Moon’s not full until 2pm, when its ecliptic longitude is opposite to that of the Sun.”

Hoping to save his pride, he replies, “But the Moon looks completely illuminated.”

“It’s never one hundred percent illuminated,” his date says, unfazed. She’s a tough cookie. “Oh, and on this side of the world it’ll be a corn moon.”

Pretending to check his watch, the young man gets confused. He remembers his science teacher explaining that the Moon reflects sunlight and that it is full when it is on the other side of the Earth from the sun, but the nighttime half of the Earth is on the opposite side of the Sun, so how could that be 2pm? Did the newspaper say it would be a full moon tonight, or did it say tomorrow night? And what’s a corn moon?

There’s only one thing he can do: look it up on Wolfram|Alpha!

One of the latest features added to Wolfram|Alpha is more coverage of full moons and other Moon phases. Back when people got their information from only a local newspaper, it was relatively simple to say that one night or another would be a full moon, because for a specific location, the time of a full moon would be closest to midnight on that day. But now it is easy to get your information from a newspaper that is far away, so its date can be off by a day. Of course, Wolfram|Alpha detects your location, so it is able to predict the date of the next full moon in your area, and the “Precise time” button reveals the exact time the full moon will take place.

corn moon 2012

Remember that because of time zone differences, there is always part of the world that is on a different day. And that affects labels like “corn moon”, which is the first full moon in September. The beginning and ending dates of September depend on the time zone, and sometimes the full moon is close to this boundary. The next ambiguous corn moon will be in 2012. More »

July 12, 2011– 8

Today we are pleased to unveil the Wolfram Genealogy & History Research Assistant and the Wolfram Personal Finance Assistant Apps for iOS! These new additions to Wolfram’s wide offering of specialized apps are the first in our series of Personal Assistant Apps, which use Wolfram’s vast knowledge base to enrich topics that matter most to you. Explore the world of your ancestors with the Wolfram Genealogy & History Research Assistant, the only tool that lets you discover what was going on while they lived. Map family relations and expand on what you already know about any of your ancestors with a simple, easy-to-use interface. It’s as if you’re traveling through time with the tips of your fingers.

Genealogy & History Research Assistant App One way you can use the Wolfram Genealogy & History Research Assistant is to track the name popularity of your family members using the app’s specialized menus. More »

July 8, 2011– 6

For thousands of years, people have been making music: banging, blowing, bowing, and strumming away as soloists or in groups. With music being an integral part of culture, it is not hard to imagine that the invention and evolution of various musical instruments is a key indicator of human ingenuity. Each instrument is unique, its physical and sonic characteristics often emblematic of the culture from which it emanates.

Wolfram|Alpha now provides a significant amount of information about a myriad of musical instruments. Ask Wolfram|Alpha about any set of instruments to get a side-by-side comparison of parameters and characteristics.

Comparing alto sax and clarinet

For many instruments, you will notice two pods for range: “Written range” and “Sounding range”. This is because in standard music notation, some instruments are written differently than they sound; these are called transposing instruments. In many ways, it is a terribly confusing notion. A score displays a certain pitch, but the pitch the instrument produces may be higher or lower. Wolfram|Alpha illustrates this difference by displaying the pitch range (along with the corresponding frequencies and keys on a piano keyboard) for how the instrument is written as well as how it sounds. For example, the flute is a non-transposing instrument and is “written as sounds”. However, its close cousin, the alto flute, sounds a perfect fourth lower than written. Still unclear? Click the “play alto flute range notes” in the written range and sounding range pods to hear the difference. Or, you can ask Wolfram|Alpha to give you the interval between the bottom note of the written range and the corresponding sounding note by querying “interval of C4 and G3“.

Interval of music notes c4 and g3

More »

July 7, 2011– 1

A few weeks ago, we pointed out some new additions to Wolfram|Alpha from the World Bank’s World Development Indicators database, primarily focused on labor and employment around the world. We’ve also incorporated data about doing business in most countries, collected by a World Bank project called, appropriately, “Doing Business.

This data covers a wide range of issues, including import/export costs, business tax rates, and the time required to complete various business-related activities. Try the following examples to get a better sense of the breadth of this dataset:

Wolfram|Alpha can also rank countries according to a number of business-related indices. Ask about the ease of doing business in Eurozone countries, for example, and you’ll see that Ireland and Greece occupy the ends of this spectrum. In this case, a higher index score indicates a regulatory environment that is generally unfriendly to business operation; in light of Greece’s recent economic woes, it should come as no surprise to see that country at the bottom of the list. (Note that for all the properties in this dataset, you can click the “Definition” button in the input interpretation or in other pods to get more details on each property.)

Ease of doing business in Eurozone countries

More »

July 5, 2011– 3

The warm summer weather provides a great opportunity to explore a new city on foot! Using OpenStreetMaps in Wolfram|Alpha, you can map out computations and comparisons of some of the world’s most famous streets and explore places of interest.

Rodeo Drive

Doing some shopping on Fifth Avenue? Walking the street for its entire length will take you 200 minutes! An African Burial Ground National Monument and Theodore Roosevelt’s birthplace are also within a mile of this route. If the trip is wearing you down, Bronx-Lebanon Hospital is only 2 miles away. More »

June 28, 2011– 9

Today we are pleased to share that ChaCha, the #1 free real-time question and answer service, has enhanced the depth, accuracy, and speed of its online and mobile Q&A service by adding computational knowledge from Wolfram|Alpha. The Wolfram|Alpha integration provides ChaCha users with instantly computed facts and answers to questions from over 100 topic areas, such as demographics, definitions, mathematics, geography, and celebrity facts.

ChaCha has historically used people to answer difficult questions to ensure a high-quality answer. We think ChaCha’s decision to incorporate Wolfram|Alpha, the world’s largest curated data repository, made accessible via free-form queries, is a natural extension of ChaCha’s service. Our match up with ChaCha also opens up Wolfram|Alpha to the larger community serviced by SMS mobile text messaging.

“At ChaCha we are constantly looking at ways in which we can better our users’ experience and provide the fastest and most accurate answers to their questions,” said Scott Jones, ChaCha’s CEO. “By partnering with Wolfram|Alpha and tapping into their vast database of computational knowledge, we are enhancing the scope and efficiency of our service.”

On the first day of integration, Wolfram|Alpha answered 32,000 of ChaCha’s incoming questions in a wide range of topics through ChaCha’s SMS service and mobile app. For example, need some quick homework help? Text “what is the inverse of Xlog3(4)?” to 242-242, and in just seconds ChaCha will text you the correct answer:

"What is the inverse of Xlog3(4)?" answered via ChaCha SMS

Or download the ChaCha mobile app and get Wolfram|Alpha-powered responses, such as “How old is Snoop Dogg?”:

"How old is Snoop Dogg?" answered via the ChaCha mobile app

We’re looking forward to providing unique and dynamically computed facts to the ChaCha Community!

June 21, 2011– 3

You can like us on Facebook, you can tweet with us on Twitter, and now you can follow us on Tumblr!

Wolfram|Alpha Tumblr

Now on your Tumblr dashboard, in between animated gifs of cats, fun graphs, and even more pictures of cats, you will find timely data, daily fun facts, and dynamic charts, all computed from Wolfram|Alpha.

Are you already using Wolfram|Alpha to add insight into your Tumblr posts? Be sure to use the official Wolfram|Alpha Tumblr hashtag: #WolframAlpha.

June 17, 2011– 8

Our ever-growing family of Wolfram|Alpha-powered iOS apps is gaining two new additions today, including the first in our new Professional Assistant series, as well as another entry in our Wolfram Course Assistant Apps. Launching today for iPod touch, iPad, and iPhone are the Physics I Course Assistant and the Network Admin Professional Assistant App. We designed our Professional Assistant Apps with working professionals in mind. They include content specific to each profession and reference information a professional may look up over the course of a normal day.

The Network Admin Professional Assistant is a useful addition to a network admin’s IT toolbox, whether at home or on the job.

Network Admin Professional Assistant
More »

June 16, 2011– 0

The early development of Wolfram|Alpha showed us that people from diverse domains of knowledge—chemistry, finance, medicine, economics, and many others—were wrestling with many of the same issues: data aggregation and curation, crowd-sourcing, data ontologies, privacy, and more. In 2010, we decided that the leaders of this global data community could benefit from a new forum to share ideas, innovations, and insights into the modern business (and science) of data. And so the Wolfram Data Summit was born, bringing together an elite group of data luminaries for an unprecedented, multidisciplinary conference.

The first annual Data Summit far exceeded our expectations, in the quality of presentations and the intensity of cross-domain debate and discussion. With so many attendees eager to continue this conversation, and so many more data innovators we wanted to invite, we knew we had to make this an annual event.

So we’re pleased to announce that the second annual Wolfram Data Summit will be open to a larger and more diverse group than last year, while maintaining the same high caliber of attendees. We will delve into new topics of general interest—apps and the mobile revolution, social network data, real-time data—while also returning to some of the key themes developed in the first Data Summit and providing more opportunities for open discussion and networking among participants.

More detailed information is available here, including the rapidly filling list of confirmed attendees. Further information, including more details on topics and schedules, will be available soon. The Wolfram Data Summit is an invitation-only event, but interested parties may request an invitation.

June 15, 2011– 3

We have been working on making Wolfram|Alpha Widgets more customizable so that it’s easier for bloggers and webmasters to incorporate them in their sites and posts. We’re now pleased to share a few updates with you.

The most exciting new feature is the pre-computed “inline” widget. With these widgets, readers get computational knowledge from Wolfram|Alpha directly, without even clicking a button! As a new twist on the iframe-style widgets, you can now choose to hide or show the inputs as well as hide or show results right on the page as a streamlined addition to your own content.

Here are some examples:
More »

June 9, 2011– 2

New York City. Los Angeles. Chicago. Each of these cities is renowned for a diverse array of cultural, entertainment, culinary, and other experiences—as well as for legendary traffic delays. But just how bad do native commuters have it? And if you drive to work in a different city, how does your commute stack up? Wolfram|Alpha can’t yet guide you through the traffic, but it can visualize and compare statistics about traffic and urban transportation in more than 100 US urban areas, with data from the Texas Transportation Institute’s Urban Mobility Report.

Ask Wolfram|Alpha about traffic in NYC, LA, and Chicago, for example, to see how they compare:

Traffic in NYC, LA, and Chicago
More »

June 7, 2011– 3

Early on June 7, 2011, the Sun once again showed signs of waking up from the last solar minimum: it unleashed a powerful solar flare. The x-ray emission from this flare can be seen in Wolfram|Alpha:

Solar flares 3 am June 7, 2011 to 3 pm  June 7, 2011
More »

June 7, 2011– 3

Today we are pleased to announce the Wolfram Tides Calculator and Wolfram Fractals Reference Apps for iPhone, iPod touch, and iPad. These are the first two in our series of reference apps that utilize Wolfram|Alpha technology to shed light on some fascinating subjects. Like our series of Wolfram Course Assistant Apps, the Wolfram Reference Apps are each designed with an optimized interface and specialized keyboards to enhance usability for mobile users.

The Wolfram Tides Calculator will become your go-to guide for tide information. Calculate the present tide or today’s high and low tides, do historical computations, or plan your vacation using the tide forecast. The app can automatically detect your current location or provide data from around the world.

Wolfram Tides Calculator App for iPad

For example, with the Tides Calculator you can enter a future date and location to see the tide forecast for a specific date. Here is the prediction for tides in Miami on July 4:
More »

June 1, 2011– 4

What do you get when you cross a mountain climber with a mosquito? Nothing—you can’t cross a scalar with a vector!

But what do you get when you cross two vectors? Wolfram|Alpha can tell you. For example:

Cross product of (1, 2, 3) and (4, 5, 6)

And in fact, Wolfram|Alpha can give lots of information on vectors. A vector is commonly defined as a quantity with both magnitude and direction and is often represented as an arrow. The direction of the arrow matches the direction of the vector, while the length represents the magnitude of the vector. Wolfram|Alpha can now plot vectors with this arrow representation in 2D and 3D and return many other properties of the vector.
More »

May 26, 2011– 13

Today we released the new Wolfram Statistics Course Assistant App for the iPhone, iPod touch, and iPad. If you are a student of introductory statistics, the probability that you’ll love the all-new Wolfram Statistics Course Assistant is pretty high! The app will help you better understand concepts such as mean, median, mode, standard deviation, probabilities, data points, random integers, random real numbers, and more.

Wolfram Statistics Course Assistant for iPad

Learning about the normal or binomial distribution? This app will show you the probability density function as well as the cumulative density function and other information.
More »

May 24, 2011– 7

Ah, spring! The time of year when winter coats are exchanged for short sleeved shirts, space heaters for open windows, and winter colds for stuffy noses, rashes, and itchy or watery eyes. When suffering from any set of symptoms, misery often seeks company, and what better way to find out how many other people share in your seasonal symptomatology than through Wolfram|Alpha? By aggregating survey data from the Centers for Disease Control and Prevention (CDC), our medical content team has put together a unique set of symptom-searching tools that will enable you to investigate all of the symptoms you may experience throughout the year. For example, by entering “sneeze”, you can immediately find that an estimated 960,000 patients complain of sneezing when they visit the doctor each year, and that marginally more male patients complain of sneezing than female patients.

Sneeze
More »

May 23, 2011– 3

Recently, CNNMoney published stories highlighting the “20 most profitable companies” and those considered to be the “20 biggest money losers”. Companies such as Exxon Mobil, AT&T, Apple, and Verizon were ranked by their 2010 profits, with each of the 20 profitable companies bringing in well over a billion dollars.

Using the information provided by both articles, there are many opportunities to gain more data on each of the companies from Wolfram|Alpha. For example, Exxon Mobil topped the list of most profitable companies, but has it always been profitable? Entering “Exxon earnings” into Wolfram|Alpha produces data and graphs documenting its earnings history.

Exxon earnings
More »

May 20, 2011– 8

To mark the second anniversary of the launch of Wolfram|Alpha, I did an interactive webcast:

Here’s a transcript of my introduction:

[Note: here is what I wrote for Wolfram|Alpha's first anniversary a year ago.]

So, as of today, Wolfram|Alpha has officially been out in the wild for two years.

And I’m happy to say, it’s doing really well.

You know, I’d been thinking about building Wolfram|Alpha for more than 30 years.

And I’ve been working to build the stack of ideas and technology to make it possible for nearly that long.

At the beginning, I was not really sure that Wolfram|Alpha was going to be possible at all.

And I think if I look a year ago from now my main conclusion was that after a year out in the wild, we’d proved that, yes, Wolfram|Alpha was indeed possible.

Well, now that we’re two years out, I think my conclusion is: Wolfram|Alpha is even a lot more important than I thought it was.

This effort to make all our knowledge computable is really something very fundamental, that’s sort of inevitably going to be needed just all over the place.

So what have we been up to this year?
More »

May 18, 2011– 3

It is hard to believe that just two years ago today Wolfram|Alpha was released for free on the web. It’s been another big year for our mission of making all of the world’s knowledge computable. Since Stephen Wolfram’s first annual update, we’ve been introducing curated data at an unprecedented rate, developing new site features and releasing a host of new developer and consumer products.

We’ve compiled a list of some of the new features, products, data, and capabilities we’ve added over the last year. You can explore this list here.

To expand on what we’ve been working on this year, Wolfram|Alpha’s creator Stephen Wolfram will take your questions in a live Q&A webcast today at 1pm EDT. We hope you will join us!

Thank you for making Wolfram|Alpha’s second year an exciting and creative time. We can’t wait to show you what’s next.

May 17, 2011– 24

Plotting functions in the Cartesian plane is such a simple task with Wolfram|Alpha: just enter the function you are looking to graph, and within seconds you will have a beautiful result. If you are feeling daring, enter a multivariate function, and the result will be a 3D Cartesian graph. Wolfram|Alpha is certainly not limited to Cartesian plotting; we have the functionality to make number lines, 2D and 3D polar plots, 2D and 3D parametric plots, 2D and 3D contour plots, implicit plots, log plots, log-linear plots, matrix plots, surface of revolution plots, region plots, list plots, pie charts, histograms, and more. Furthermore, in Wolfram|Alpha we can generate specialized plots for illustrating asymptotes, cusps, maxima, minima, inflection points, saddle points, solutions of ordinary differential equations, poles, eigenvalues, series expansions, definite integrals, 2D inequalities, interpolating polynomials, least-squares best fits, and more. Let’s take a look at the plotting functionality in Wolfram|Alpha, some of which is newly improved!

We will start simple with 2D Cartesian plots.

Here we plot sin(√7x)+19cos(x) for x between -20 and 20.

Plot sinsqrt7x+19cosx between -20 and 20
More »

May 13, 2011– 31

Blog anniversary

Another year has flown by here at Wolfram|Alpha, and the gears are really turning! New data and features are flowing at a rapid rate. To celebrate, Wolfram|Alpha’s creator, Stephen Wolfram, will share what we’ve been working on and take your questions in a live Q&A.

Please join us on Facebook or Wolfram|Alpha’s Livestream on Wednesday, May 18, 2011, at 10am PDT/12pm CDT/1pm EDT/6pm BST.

If you have a question you’d like to ask, please send it as a comment to this blog post or tweet to @Wolfram_Alpha and include the hashtag #WAChat. We’ll also be taking questions live on Facebook and Livestream chat during the webcast.

We’re looking forward to chatting with you on May 18!

May 13, 2011– 6

Do you need some help navigating your chemistry or precalculus classes? Or maybe you’re still trying to decide which classes to take this fall. Good news! Today, we’re releasing the Wolfram General Chemistry and Precalculus Course Assistant Apps, two more Wolfram|Alpha-powered course assistants that will help you better understand the concepts addressed in these classes.

If you’re taking chemistry, download the Wolfram General Chemistry Course Assistant App for everything from looking up simple properties like electron configurations to computing the stoichiometric amounts of solutes that are present in solutions of different concentrations. This app is handy for lab researchers, too!

General Chemistry Course Assistant

The specialized keyboard allows you to enter chemicals by using formulas or by spelling out their names.
More »

May 6, 2011– 6

In 2010, our friends at the World Bank opened up their highly regarded World Development Indicators (WDI) database, making hundreds of economics, education, health, and other indicators free to download and explore. As part of our own mission to make data more accessible and comprehensible, we’re pleased to announce that we’ve been steadily adding WDI and other World Bank data to Wolfram|Alpha, so you can answer thousands of new questions about key components of global development.

One of the first sets we tackled was data on labor and employment, which means Wolfram|Alpha can now generate some quite detailed computations and comparisons of employment-related data for most of the world’s countries and territories. Try an input like “fraction of people working in agriculture in US, Russia, and Japan” to see find out how much less agrarian these economies have become over time. More »

May 4, 2011– 7

In light of the accident at the nuclear facility in Fukushima, Japan following the earthquake and tsunami on March 11, 2011, there has been an increased interest about nuclear power and nuclear reactors worldwide. Due to the desire for factual information about this important topic, we have added data on commercial nuclear power reactors—based on information from the International Atomic Energy Agency (IAEA)—to Wolfram|Alpha.

The IAEA’s database has information on all of the world’s commercial nuclear power plants, including those currently operating, those that have been shutdown, and reactors under construction. Ask Wolfram|Alpha for “all nuclear reactors”, and it is evident that nuclear power is a widely used source of electrical energy.
More »

May 2, 2011– 1

There are more than four million births per year in the US alone. And just in time for spring, a time associated with new life, Wolfram|Alpha’s research team has introduced a unique set of tools to help soon-to-be mothers and fathers better understand what is happening to their developing fetuses throughout pregnancy.

One of the most common methods of monitoring fetal development is through ultrasounds. Besides providing first glimpses of the baby, ultrasound images also provide doctors and technicians with important information about the fetus’s physical development. This information is useful in helping doctors diagnose, predict, and potentially avoid complications further down the line in pregnancy. To find out the typical measurements of a fetus for a given gestational age (e.g. 21 weeks), try entering something like “pregnant 21 weeks” into Wolfram|Alpha.

For the gestational age of 21 weeks, Wolfram|Alpha can tell you the estimated fetal weight, the normal range of fetal weights, and the estimated dates of conception and birth.

Pregnant 21 weeks
More »

April 28, 2011– 4

Everyone needs a little break when preparing for finals! That’s why we’re giving you a special break on all Wolfram Course Assistant Apps now through Sunday, May 1, 2011.

Wolfram Course Assistant Apps will help you grasp key concepts and gain better understanding of the answers, all of which will have you feeling confident and prepared to ace your final exams!

Wolfram Algebra Course Assistant for iPad

The following Wolfram Course Assistant Apps are available for the iPhone, iPod touch, and iPad:

Wolfram Algebra Course Assistant, now $0.99 (US)

Wolfram Calculus Course Assistant, now $1.99 (US)

Wolfram Music Theory Course Assistant, now $0.99 (US)

Wolfram Astronomy Course Assistant, now $2.99 (US)

Wolfram Multivariable Calculus Course Assistant, now $2.99 (US)

Best of luck with your finals! Our team is developing an app for every course, so be sure to check back for more helpful Wolfram Course Assistant Apps before heading to class next semester.

April 27, 2011– 4

Wolfram|Alpha is a powerful tool for finding information about the universe at large, but sometimes we are interested in a much smaller universe: our families. Genealogical research is an increasingly popular hobby, and one which Wolfram|Alpha can make easier using features across several of its subject areas.

We blogged last year about how Wolfram|Alpha can map family relations, which can certainly be more helpful the further your genealogical research takes you from the trunk of your family tree. Recently, another researcher (and previously unknown relative) contacted me. This new connection sent me straight to Wolfram|Alpha to determine our relationship. Her great grandfather was my great grandfather’s brother and, thanks to Wolfram|Alpha, I learned that she is my third cousin.

Great granddaughter of my great great uncle
More »

Tags:
April 25, 2011– 8

Wolfram|Alpha is written in Mathematica, which as its name suggests is a fantastic system for doing mathematics. Strong algorithms for algebraic simplification have always been a central feature of computer algebra systems, so it should come as no surprise to know that Mathematica excels at simplifying algebraic expressions. The main two commands for simplifying an expression in Mathematica are Simplify and FullSimplify. There are also many specific commands for expressing an algebraic expression in some form. For example, if you want to expand a product of linear polynomials, Expand is the appropriate function.

The good news is that everyone has access to the power of Mathematica‘s simplification and algebraic manipulation commands in Wolfram|Alpha. We will now outline some of these features in Wolfram|Alpha, starting with the expression:

Mathematical expression

and we will use Wolfram|Alpha to break it down to something significantly much simpler.
More »

April 18, 2011– 5

By popular demand, Wolfram|Alpha recently expanded population data for most of the world’s countries, based in part on statistics from the United Nations Population Division. Populations are shaped by factors such as disease, war, genocide, and famine as well as more benign phenomena such as immigration. One of the more common user requests in this area has been to support queries like “China population distribution”, which now returns an age pyramid and detailed table of population by age and sex:

China population distribution

You can also query for specific age groups, as indicated on the pyramid, or just query for a single age, and Wolfram|Alpha will return data for the appropriate five-year age “bin”:
More »

April 18, 2011– 10

Today, in conjunction with DuckDuckGo, we are happy to share that Wolfram|Alpha and DuckDuckGo have entered a new phase of our relationship as official partners. As a result of this partnership, DuckDuckGo will expand Wolfram|Alpha integration into its search site and will maintain the now-official Wolfram|Alpha API Perl binding.

Users of the up-and-coming search site DuckDuckGo know that the site is unique because it doesn’t track history, contains less spam, features a cute bow tie-wearing duck, and provides zero-click information that immediately pops up under the search box. Since the release of the Wolfram|Alpha API, DuckDuckGo has been gradually integrating Wolfram|Alpha’s computational knowledge engine into its offerings, providing users with dynamically computed facts.

DuckDuckGo -- population of metro Atlanta

Our friendship began when Gabriel Weinberg, Founder of DuckDuckGo,  volunteered to be an early Wolfram|Alpha tester. He went on to develop the now-official Wolfram|Alpha Perl API binding and began featuring select Wolfram|Alpha functionality on DuckDuckGo.

“Integrating Wolfram|Alpha into DuckDuckGo was a no-brainer decision, as it can provide instant answers for a broad range of general search queries that are otherwise not easy to get answers to. That’s because Wolfram|Alpha does deep processing of a lot of non-web datasets”, said Weinberg.

“Our primary goal with the launch of version 2 of the API in January was to open Wolfram|Alpha to all developers and their broad spectrum of clever ideas”, said Wolfram|Alpha’s Schoeller Porter, Architect, Developer Relations. “Gabriel and DuckDuckGo exemplify the entrepreneurial spirit by integrating Wolfram|Alpha’s computed knowledge into web search in a compelling, relevant, and ingenious way. We’re excited to be a part of DuckDuckGo’s continued growth”. More »

April 15, 2011– 4

Last year, we showed you how Wolfram|Alpha could help you explore some interesting historical statistics about federal income taxes in the United States. We’ve picked up the latest available figures from the Internal Revenue Service (IRS) through the 2008 tax year, so you can revisit that data and see if previous years’ trends have held up.

Wolfram|Alpha still can’t do your taxes (and if you haven’t finished them yet, don’t forget you’ve got until Monday to file)… but it can compute some very interesting new facts about income taxes in the US. There’s been a lot of discussion and debate this year about state-level corporate and individual taxes and their impact on budgets and the overall business climate in any given state. So we’ve added data on the maximum and minimum individual and corporate tax rates in each US state, which means Wolfram|Alpha can now compute rankings and summary statistics about “income tax rates in US states” or perform a comparison of the “highest corporate income tax rates in Illinois, Iowa, and Indiana”.

Highest corporate income tax rates in Illinois, Iowa, and Indiana More »

April 12, 2011– 3

Vacation planning season is upon us! Planning a vacation is no easy feat, but Wolfram|Alpha can help. With data on airlines, gas prices, weather, and currency, taking a trip has never been easier.

Let’s say you’re researching locations to take a family vacation and you want to know the average temperature of the locations at a specific time of year. Query something like “temperature May Hilton Head, Miami” to compare two locations’ average temperatures for that month.

Temperature May Hilton Head, Miami More »

April 7, 2011– 5

Today the Wolfram|Alpha App for Android is the featured free app of the day in the Amazon Appstore! You can grab the app for your Android mobile device for free here.

Amazon Appstore for Android

The Wolfram|Alpha App for Android allows you to access expert knowledge on the go. Use the app’s specialized math keyboards, charts, and graphs adapted for mobile screens; support for native voice input; and location awareness to take full advantage of Wolfram|Alpha on your mobile device.

Android app voice commandAndroid app sky chart

Don’t wait—the app is only available as the featured free app until the end of the day!

April 5, 2011– 4

If you’re concerned about the US economy, you probably caught last week’s news that Standard & Poor’s Case–Shiller home price index for 20 large cities continued to decline in January. If you’re curious to know more about recent housing trends in the US, you can not only ask Wolfram|Alpha about the 20-city index, but also for details on any of the major metropolitan areas included in that composite. For example, query “Las Vegas, Phoenix, Los Angeles, Miami Case–Shiller index”, and you can see just how big the housing “bubble” was in each of these four cities.

Las Vegas, Phoenix, Los Angeles, Miami Case–Shiller index
More »

April 1, 2011– 26

When we released Wolfram|Alpha “into the wild” nearly two years ago, we did so knowing that user input would help shape the future of our grand experiment. Since then, we’ve implemented literally thousands of user suggestions and have continually refined our ability to understand and precisely answer natural-language questions across virtually every domain of human knowledge.

When we launched, our strongest areas of knowledge were definitely in mathematics and science, but we’ve steadily increased our coverage of data in more popular “everyday” areas: information about health and medicine, housing prices, movies, school districts, jobs, crime, and much more.
More »

March 31, 2011– 4

Today we are releasing Wolfram Multivariable Calculus and Wolfram Astronomy, the next two apps on a growing list of Wolfram Course Assistant Apps. These course assistants will help students learn their course material using the power of Wolfram|Alpha.

The Wolfram Astronomy Course Assistant allows you to easily look up information on constellations and planets, but it can also calculate anything from the next lunar eclipse to the solar interior.

Wolfram Astronomy Course Assistant Hertzsprung-Russell diagram
More »

March 31, 2011– 15

By now, you’ve probably noticed those cute black and white squares popping up on everything from T-shirts to magazine advertisements to cereal boxes. These are called Quick Response (QR) codes, and thanks to the rise in smartphone use, they are becoming more popular than ever.

Scan these codes with a QR reader

Scan these codes with a QR reader Scan these codes with a QR reader

Since their inception in 1994 in Japan, QR codes have quickly risen in popularity throughout many Asian countries. The technology is still finding its footing in the United States and other western countries, but many advertisers and niche communities are adapting the 2D barcode innovation. Flip open your favorite magazine and you will most likely see the stamp-like code on multiple advertisements.

Wolfram|Alpha now offers the capability to produce QR codes. Just type in “QR code” in addition to whatever information you want to be coded. The function can encode up to 7 KB of data, including phone numbers, email addresses, URLs, or just plain text.
More »

March 29, 2011– 2

Spring has officially sprung, and here in the Midwest, we’re eagerly ice picking our way out of hibernation for some fun in the Sun! Some of us are enjoying the extended daylight hours, and others are jetting off to tropical spring break destinations.

While we were nestled by our office heaters, drinking Swiss Miss, and dreaming of the bright sunshine, we developed a few new tools in Wolfram|Alpha that give you facts on how to keep your skin healthy while enjoying the Sun. To get started, simply query “time to sunburn”. This query allows you to calculate how long your skin can be exposed to the Sun without burning based on your skin type, location, time, the level of Sun protection factor (SPF) you might be using, and how long you stay in the Sun. You can also select “UV index” for results based on the UV index, your skin type, SPF, and time in the Sun.

Time to sunburn

The personalized results show how long you can stay in the Sun before you’re likely to burn based on the factors you reported, a Sun protection advisory recommending an SPF level, and a UV forecast for your location. More »

March 23, 2011– 2

Do you need to work with numbers that are of the magnitude of thousands, millions, or even billions? How about the thousandths, millionths, or billionths? Scientists and engineers need to work with really large and really small numbers every day. Now Wolfram|Alpha can help put all of those large and small numbers into scientific notation. For example, the Earth’s mass is about 5973600000000000000000000 kg, but it is nicely represented in scientific notation as 5.9736×10^24 kg.

5973600000000000000000000 kg to scientific notation
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March 16, 2011– 8

One of the most commonly used materials all around us is wood. There are many different kinds of woods with wide ranging mechanical, physical, and thermal properties, which make them suitable for different applications. From building houses to making kitchenware, wood is an ideal and easy to use material. In general, wood is broadly available at reasonable prices and is easily formable, making it desirable for construction work. Of course, depending on the application, different properties of wood are desirable. For example, for building a house with wood, high strength is desired, whereas for making a cutting board, you probably want something that has a harder surface so it doesn’t get dented easily. Wolfram|Alpha now has a large database of all kinds of wood and their various properties.

There are various ways you can obtain data on woods using Wolfram|Alpha. If you need to quickly skim through the different kinds of woods, Wolfram|Alpha can generate a quick report of properties of a certain kind of wood.

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March 14, 2011– 7

Yes, it is once again the time of the year when the mathematically inclined gather together to celebrate Pi Day

Pi Day

…and, in the process, swap trivia of note on everyone’s (including Wolfram|Alpha’s) favorite number.

There have been no shortage of blog posts already written on the subject; see, for example, last year’s “Pi Day in Wolfram|Alpha” (or the Wolfram Blog Pi Day posts from 2008 or 2010). As already hinted at in last year’s blog, one would expect the pi to be ubiquitous in a computational knowledge engine—and so it is. Therefore, at the risk of beating a proven transcendental constant to death, this year we offer a few (well, OK: more than a few) additional pi-related esoterica courtesy of Wolfram|Alpha.
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March 9, 2011– 6

Remember those dynamic calculators we mentioned back in November?

Well, they’re back… with more features! We’ve released a whole new batch of calculators that cover some different areas of math.

For those who don’t remember, in November, we released calculators capable of computing integration, limits, date differences, and more. With this new slew of calculators, we are covering some other commonly asked math concepts, like vector and matrix manipulation, GCD, LCM, inverses of functions, linear approximation of functions, 3D plotting, base conversions, and currency conversion.
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March 4, 2011– 4

Wolfram|Alpha recently added information about the minimum wage in U.S. states (from 1967 through today) based on data from the U.S. Department of Labor. This means you can ask Wolfram|Alpha about simple historical facts, like the U.S. minimum wage in 1980, or perform simple analyses, like comparing the current minimum wage in Ohio and Alaska.

Compare minimum wage in Ohio and Alaska More »

March 3, 2011– 1

Students of the history of science will recall learning that Galileo observed and described the periodic motion of a simple pendulum around 1602. Until being supplanted by other technologies around the first third of the 20th century, this property of pendula has been indispensible in the creation of accurate timekeeping devices.

An idealized pendulum consisting of a weight (often called a “bob”) on the end of a massless cord and suspended from a frictionless pivot is called a simple pendulum or, more explicitly, a simple gravity pendulum. Wolfram|Alpha has known about simple pendula for some time, as you can verify by entering “pendulum”. In fact, doing so brings up not one but two pendulum results:

Pendulum More »

February 25, 2011– 3

Why did the mathematician name his dog Cauchy? Because he left a residue at every pole!

But could the mathematician find the poles and their residues for a given function? He certainly could, with the help of Wolfram|Alpha.

We are proud to announce that Wolfram|Alpha has added residues and poles to its ever-expanding library of mathematical data that it can compute! To showcase this behavior, let’s first recall just what a pole is.

In the study of complex analysis, a pole is a singularity of a function where the function behaves like 1/zn at z == 0 .

More technically, a point z_0 is a pole of a function if the Laurent series expansion of the function about the point z_0 has only finitely many terms with a negative degree of zz_0. As an example, let’s look at the Laurent expansion of 1/Sin[z] at z == 2 Pi:

Laurent expansion More »

February 24, 2011– 5

One often hears such phrases like “She’s as fast as a cheetah”, or “He is slow like a sloth”. And one often also stops to ponder, “Well, how fast IS a Cheetah?” or “How laboriously slow DOES a sloth actually move?”. Wolfram|Alpha now has a slew of interesting facts about the numerous species that co-inhabit planet Earth. We recently added an overall set of more than 400 new properties, which span the most interesting and intriguing features of different species within the animal and plant kingdoms.

For starters, we can compute how much faster a cheetah is than a three-toed sloth:

Cheetah running speed/three-toed sloth running speed

It’s a pretty remarkable fact that the cheetah could nap for almost 11 hours and still beat the sloth to the finish line in a 1-mile race. More »

February 21, 2011– 5

An algorithm is, in essence, a procedure given by a finite description that solves some computational problem. The field of computational complexity deals with questions of the efficiency of algorithms, i.e. “For a computational problem X, how many steps does the best algorithm perform in solving X?” You might think that questions in this field would be confined to the realm of computer science, except for the fact that computational complexity theory contains the mathematical problem of the century! Currently, many mathematicians around the world are attempting to solve the famed open problem P vs. NP, a problem so important that it is one of the seven millennium problems of the Clay Mathematics Institute and carries a million dollar prize. In fact, according to our logs, many of you tried to ask Wolfram|Alpha this same question before this new functionality was available! But before we talk about how Wolfram|Alpha can help you become a millionaire, let us begin with a historical overview of the subject. More »

February 17, 2011– 11

Since the launch of Wolfram|Alpha Volunteer Central, we’ve been happy to work with volunteers to develop data in new areas. Today, we are showcasing the beginning of video game data, which was curated by Wolfram|Alpha volunteers.

Super Mario Bros. release date
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February 14, 2011– 8

On Valentine’s Day, love can be found everywhere, from the corner flower shop to the interwebs. We poured our heart out to Wolfram|Alpha and found that everyone’s favorite computational knowledge engine is no stranger to love…

What is love?

Love according to Wolfram|Alpha

I love you

How nice. Be assured the feeling is mutual.

Are you in love?

Yes. I love the Internet.

But what do men want?

Wolfram|Alpha isn't sure what to do with your input.

Am I pretty?

All people who allow me to compute for them are beautiful to me.

Will you be my Valentine?

Sure, if you'll be mine!

Fifth heart curve

Happy Valentine’s Day!

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February 9, 2011– 5

It’s a bit of an understatement to say that trees play vital roles in each of our lives. Trees absorb carbon dioxide from the atmosphere and release oxygen back to it. Our houses are made primarily of wood. We line our properties with trees to give us shade and privacy and also to reduce the wind that reaches our homes. Even the syrup we put on our pancakes is made from tree sap. One important species of tree, the sugar maple (Acer saccharum), is prized for both its sap and wood production. Therefore, it is important to know the growth pattern of the tree. How tall is it when it is, say, 50 years old? Thanks to data given to us by the United States Forest Service, you can now ask Wolfram|Alpha that exact question.

Click the image for the full results

Click the image for the full results

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February 7, 2011– 7

One of the most common queries on Wolfram|Alpha is a user entering his or her date of birth to see how many years, months, and days old he or she is today.

Since this feature first became popular, we added more birthday-specific features for this query type. By adding “birthday” to your query, you’ll get even more detailed information, such as a birthday countdown, a notable dates pod, and astrological birth information.

For example, submit a query such as “birthday March 29, 1990” to see how many days there are until your next birthday (time to start planning, March 29ers!) and how long it’s been since your last birthday.

Birthday March 29, 1990
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February 3, 2011– 2

We normally don’t think about how involved alloys are in our day-to-day lives, but the roads and bridges we take to get to work, our cars, cell phones, computers, and even our homes and furniture often contain alloys. And people who create these objects need access to reliable and trustworthy sources of information about the physical properties of all types of alloys, so they can choose the right material for a particular application.

That’s why we’re pleased to announce that Wolfram|Alpha can now provide detailed information about more than 11,000 kinds of alloys, in response to simple, natural-language queries:

UNS G10500 tensile yield strength
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February 2, 2011– 4

We’ve been having so much fun over the past few months hunting for fun facts in Wolfram|Alpha that we thought it was time to give @WolframFunFacts its very own space in the Twitterverse.

Meet Fun Facts Spikey

Meet Fun Facts Spikey

For those of you who are new to Wolfram Fun Facts, they are unique facts computed from Wolfram|Alpha’s trillions of pieces of data. All of this knowledge is built upon a computational engine that allows us to mash up topic areas such as people, finance, dates, and more to do impressive, if not outrageous, computations.

Here are just a few fun fact samples we’ve discovered in Wolfram|Alpha:

We’ll be sharing all of the fun facts that we, and you, discover every day. Follow @WolframFunFacts and tweet us your favorite #funfact!

January 28, 2011– 8

It is immediately clear to anyone who has used the site that Wolfram|Alpha knows a lot about mathematics. When computing integrals, sums, statistics, properties of mathematical objects, or a myriad of other mathematical and mathematics-related problems, it typically returns an extensive and exhaustively complete result. Which is of course not surprising, given that Wolfram|Alpha has the entire power and knowledge of Mathematica behind it, especially when combined with the fact that this native “smarts” is further augmented with large amounts of curated data and customized processing.

However, many visitors to the site have noted in the past that Wolfram|Alpha had relatively little computable knowledge about mathematical terms themselves, a state of affairs in contrast to its knowledge of words in the English language, and perhaps surprising in light of the existence of another Wolfram site devoted to the definition and description of terms in mathematics, namely MathWorld.

As readers of MathWorld likely already know, the entire MathWorld website is written and built using Mathematica. It has therefore been possible to programmatically process the entire 13,000+ entries comprising MathWorld into the native data format of Wolfram|Alpha, thus exposing its content in more computable form.

As an example of the sort of new knowledge this confluence brings to Wolfram|Alpha, consider the input “Lorenz attractor”. In the past, this would simply bring up a Wolfram|Alpha future topic page.

With the incorporation of MathWorld content, the default parse now goes to a description of the attractor, complete with an illustrative figure and some helpful typeset equations:

Lorenz attractor

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January 26, 2011– 5

When we are growing up and learning about the world, there are moments when a topic or idea really catches our attention. Perhaps it is while reading a book or during a lecture given by a good teacher. For me, one of those moments occurred during my junior year of high school in Mr. Brooks’s chemistry class. We were learning about the structure of the atom, and Mr. Brooks did a demonstration for us. He turned off the lights in the classroom and turned on a hydrogen discharge tube. The tube glowed with a pink light. Then Mr. Brooks put a prism in front of the glowing discharge tube, and several vertical lines of light appeared on the chalk board behind the prism.

At the time, I didn’t really understand that the voltage applied across the discharge tube was exciting the electrons around the hydrogen atoms and that the lines formed as the pink light passed through the prism were characteristic wavelengths of light being emitted as the electrons around the hydrogen atoms returned to lower energy levels. But I clearly remember the intense curiosity I felt about the phenomenon I was witnessing. It is, therefore, with some nostalgia that I announce the addition of the National Institute of Standards and Technology’s (NIST) atomic spectra database to Wolfram|Alpha.

Investigation of atomic spectra contributed significantly to our understanding of atomic structure and are described by the Rydberg formula. Furthermore, atomic spectra are used by astronomers to classify and determine the composition of stars. Today, the NIST database has become the most comprehensive and reliable set of data for atomic spectra and includes information about spectral lines and atomic energy levels associated with many elements and ions. All of this data can now be found in Wolfram|Alpha, including that visible hydrogen spectrum I was so curious about in high school:

Click the image to see the full results

Click the image to see the full results

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January 20, 2011– 11

Wolfram|Alpha is making possible a whole new very interesting and very powerful kind of computing. And with the release today of version 2.0 of the Wolfram|Alpha API, it’s going to be considerably easier for a broad range of software developers to take advantage of it.

I’m happy to say that it seems as if Wolfram|Alpha is pretty useful to humans—for example through the wolframalpha.com website. But it also turns out that Wolfram|Alpha is extremely useful to programs. And in fact, even today, the number of requests coming to Wolfram|Alpha each second from programs often exceeds by some margin all the requests coming directly from humans.

The reason for this popularity is really pretty simple: Wolfram|Alpha completely changes the economics of a lot of programming. You see, these days a remarkable number of programs rely on having some kind of knowledge. And traditionally, the only way to get knowledge into a program was for the programmer to painstakingly put it there.

But with Wolfram|Alpha in the picture, it’s a different story. Because built into Wolfram|Alpha is already a huge amount of computable knowledge. And if a program is connected to Wolfram|Alpha, then it can immediately make use of all that knowledge.

Whether one’s building a website or a mobile app or desktop software or an enterprise application, the point is that one can use Wolfram|Alpha as a “knowledge-based computing” platform—so that having all sorts of computable knowledge becomes effectively free from an engineering point of view.

How does a program communicate with Wolfram|Alpha?  It uses the Wolfram|Alpha API. (These days, API is pretty much a term on its own, but it comes from “Application Program Interface”.)
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January 19, 2011– 9

As kids start to return to classes after the holidays, we’re happy to announce that Wolfram|Alpha has the ability to compute some interesting information about their school districts. You can now use Wolfram|Alpha to analyze and compare data on student-teacher ratios, expenditures, revenues, and salaries in more than 18,000 public school districts in the United States.

Let’s start with an example on the West Coast: Seattle Public Schools is one of the larger districts in the country, with over 100 schools and more than 45,000 students. The student-teacher ratio is 18:1, and if you scroll down you’ll see that total expenditures are about $14,000 per student per year.

Seattle Public Schools

Click the image to see the full results

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January 12, 2011– 44

Today we’re releasing the first three of a planned series of “course assistant” apps, built using Wolfram|Alpha technology.

Wolfram Algebra

The long-term goal is to have an assistant app for every major course, from elementary school to graduate school. And the good news is that Wolfram|Alpha has the breadth and depth of capabilities to make this possible—and not only in traditionally “computational” kinds of courses.

The concept of these apps is to make it as quick and easy as possible to access the particular capabilities of Wolfram|Alpha relevant for specific courses. Each app is organized according to the major curriculum units of a course. Then within each section of the app, there are parts that cover each of the particular types of problems relevant to that unit.
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January 11, 2011– 7

Today we unveiled a new look on the wolframalpha.com site. We decided the website needed to be reorganized to allow expansion for upcoming consumer, enterprise, and developer products. 2011 is going to be an exciting year for Wolfram|Alpha!

When visiting the site you’ll notice an updated version of your home page. Once you’re there, “take a quick tour”, visit the newly redesigned product pages, and explore resources and tools.

Take a tour of Wolfram|Alpha

You may have noticed that we’re developing new features on the results pages, too. One of those features is “linked results”. For example, enter a query for “Chicago”. Notice the blue underlined links? Click one to dig deeper into Wolfram|Alpha and see more related information.

Chicago

We’re also developing “dog-ear peelbacks”. Hover over the dog-ear in the left corner of each pod to uncover how you can save the contents of the pod as an image or copyable plaintext.
Dog-ear peelback

The site’s new look is just the first of many new things to come here at Wolfram|Alpha. We’re looking forward to sharing them with you!

January 11, 2011– 2

Today we’re officially wrapping up Wolfram|Alpha’s Deck the Halls with Facts & Knowledge Holiday Gift-Away by re-opening the gallery and announcing the winners! In early December we launched the contest as a way to say thank you for making 2010 a great year for Wolfram|Alpha, and to give some fun Wolfram swag to members of our community.

To start, we gifted Wolfram|Alpha Spikey paper sculpture kits to the first 500 people to enter the contest by submitting their favorite Wolfram|Alpha fun facts. We enjoyed reading all of the clever fun facts contestants uncovered in Wolfram|Alpha. Nyth discovered that eating a serving of bacon a day for one year will result in the consumption of 2.5lbs of fat. Sri found that the average life expectancy of a tortoise is 137 years. You can dive into Wolfram|Alpha to discover a countless number of fun facts.

Contestants had the opportunity to enter photos of their Wolfram|Alpha Spikeys, along with their fun facts, in a vote-off for a chance to win prizes such as Mathematica Professional, an iPad, Wolfram mobile apps, and T-shirts. The votes have been tallied and the winners have been announced on the Holiday Gift-Away site. Congratulations to all of the winners.

Online voting contests have their share of challenges. During the vote-off we discovered a few vulnerabilities in the voting system. We put additional measures in place to help secure voting, and we promptly identified and removed votes that fell outside of the contest’s rules. Once voting closed, we conducted a second round of auditing. It was very important to us that we reviewed the data and confirmed the correct winners.

Thank you to everyone who submitted their favorite Wolfram|Alpha fun facts and Spikey photos and supported their favorite entries in the vote-off!

January 7, 2011– 3

The real line runs from negative to positive infinity and consists of rational and irrational numbers. It generally appears horizontally, and every point corresponds to a real number. Also known as a number line in school, the real line is said to be one of the most useful ways to understand basic mathematics. Wolfram|Alpha can now aid you in learning the difference between x<-5 and x>5, or Abs[x]<2.

Wolfram|Alpha now graphs inequalities and points on the real line. This new feature in Wolfram|Alpha allows you to plot a single inequality or a list of multiple inequalities. Let’s start off simply and try “number line x<100”.

Number line x<100

You can easily see that this is the set of all real numbers from negative infinity to, but not including, 100.

What if you need to plot a more difficult inequality, like “number line 3x<7x^2+2”? This plot will show that the solutions to this inequality are all real numbers between negative and positive infinity.
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January 6, 2011– 4

Consider packing circles inside a circular container, or less abstractly, placing cookie dough on a cookie sheet. In the case of cookies, which expand to be a roughly circular shape, you don’t want them so close that they run into each other. At the same time, you don’t want them too far apart, because that would mean fewer cookies.

One of the latest features of Wolfram|Alpha is the ability to get information about packing circles into circles.

For instance, suppose you have a circular baking sheet with a diameter of 12 inches, and you want to make 20 cookies. You can ask Wolfram|Alpha “pack 20 circles in a diameter 12 inch circle”; not only does it give you a diagram of the densest packing, but also the largest radius of the circular cookies on the 12-inch baking sheet.

Pack 20 circles in a diameter 12 inch circle

Or you might know the size of the cookies and want to know how many can fit? One way to get the answer would be “pack r=1 circles in a diameter 12 circle”.
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