As summer heats up, we instinctively reach for the air conditioning (AC) controls. This miracle of modern technology lets us create a cool breeze to banish the crushing heat. At the same time, AC brings soaring electric bills. How can we optimize our use of air conditioning, keeping cool while minimizing our costs?

Wolfram|Alpha provides several helpful formulas in this area, the first of which is a method for calculating the degree days for a location over a period of time. Degree days is a measure of how often the temperature was above (for cooling) or below (for heating) a given temperature or range of temperatures. It is used in a wide range of climate and energy cost-related areas, from agriculture to monitoring the heating and cooling costs of climate-controlled buildings. More »

Recently the author of xkcd, Randall Munroe, was asked the question of how long it would be necessary for someone to fall in order to jump out of an airplane, fill a large balloon with helium while falling, and land safely. Randall unfortunately ran into some difficulties with completing his calculation, including getting his IP address banned by Wolfram|Alpha. (No worries: we received his request and have already fixed that.) More »

As part of our ongoing plan to expand Wolfram|Alpha’s numerical method functionality to more kinds of algorithms, we recently addressed solving differential equations. There are a number of different numerical methods available for calculating solutions, the most common of which are the Runge–Kutta methods. This family of algorithms can be used to approximate the solutions of ordinary differential equations. More »

Spoiler Alert
Like many people, I went to see the movie Elysium last weekend. The movie’s premise is that the wealthy members of society have relocated to an orbital space station, named Elysium, that circles the Earth while the rest of humanity is stuck on a seemingly dying world.

Focusing on the science of the movie, what can Mathematica and Wolfram|Alpha tell us about the space station and some of the other events portrayed? More »

As we continue to expand the functionality of Wolfram|Alpha, we want to include not only the symbolic and exact results, but also allow you the option to explore the numerical approximations for solving mathematical problems such as differential equations and integrals. These methods, both simple and complex, continue to underpin many of our modern day calculations. More »

Last year we greatly expanded our step-by-step functionality for mathematical problems in Wolfram|Alpha. These tools can be a great aid for students to understand the methods of solving integrals and equations symbolically. But what if we are not looking for a symbolic result? What if we need a numerical approximation? For example, we might be looking at an integral or differential equation that cannot be solved in a closed form, or we might just want to find where an equation intercepts the x axis. More »

Many of us are familiar with motion in a straight line: you speed up and move faster, you travel forward and end up someplace new. But there is another type of motion: angular motion, or the motion in a circular path. These are the kinematics of a merry-go-round, a spinning top, or the orbit and rotation of the Earth. More »

Throughout the history of physics, scientists have postulated laws and theories about the nature of the world around them. Some were proven false, while others have grown to be the basis of entire fields of study. One such field is classical mechanics, which describes the area of physics most familiar to us, that of the motion of macroscopic objects, from baseballs to planets and traveling along hills to falling from space. As one of the oldest subjects in science, the work here serves as a basis for less familiar areas such as relativity and quantum mechanics. More »

Tools are a natural extension of our mastery of physics. By putting our knowledge to use, we are able to manipulate the world around us on a much larger scale. Tools and machines have allowed us to build great monuments, to settle otherwise inhospitable locations, and to launch ourselves into space. More »

Last weekend, Looper came out in theaters, bringing time travel back to the big screen. But there are lot of questions that can be asked about the science of the world it portrays. We will visit some minor spoilers along the way, so you may want to wait to read this post until you see the movie. In addition to time travel, Looper depicts widespread solar power and almost ubiquitous telekinesis. What can Wolfram|Alpha tell us about this and other aspects of the film? More »