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 z – z_0. As an example, let’s look at the Laurent expansion of 1/Sin[z] at z == 2 Pi:
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:
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 »
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 »
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.
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.
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:
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.
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:
- It would require 8.4×10^11 gallons of paint to cover the surface of the moon
- If driving a car at 60 miles per hour, it will take 11.18 million years to travel one light year
- The average American consumes 125.6 lbs of potatoes per year
- The probability that two people in a 23-person room share the same birthday is 0.51
We’ll be sharing all of the fun facts that we, and you, discover every day. Follow @WolframFunFacts and tweet us your favorite #funfact!