April 21, 2008 — Todd Rowland, Academic Director, Wolfram Science Summer School
On Sunday, April 13, 2008, John Wheeler passed away at the age of 96.
He was a central figure in twentieth-century physics, in the middle of it all, working on the H-bomb and studying black holes. His legacy in physics is continued in his influence on a vast number of students, and their students in turn.
His contributions were many. Some have found their way into Demonstrations:
|Zonohedron Turned Inside Out
|Particle Moving around
Two Extreme Black Holes
March 13, 2008 — Ed Pegg Jr, Editor, Wolfram Demonstrations Project
Pi (π, the ratio of the circumference of a circle to its diameter), its older brother the golden ratio phi (φ), and the much younger e and i are the most famous numbers in mathematics. Pi is everywhere: not only in circles and spheres, but also in the results of all kinds of integrals, sums, and products, as well as in number theory and physics. The personality of π is largely unknown: irrational, transcendental, possibly and probably normal.
Because of π’s importance, its digits (3.14159265…) have an almost cult following. The first few digits, 3.14, correspond to notation for March 14th, which was first celebrated as Pi Day in 1988, in the San Francisco Exploratorium. Wolfram Research has the most π presence on the web, with material at The Wolfram Functions Site (pi page, pi visualizations), MathWorld (pi, circle, sphere), and The Wolfram Demonstrations Project (pi, circle, sphere, disk, wheel), not to mention several built-in Mathematica symbols (Pi, EllipticPi, PrimePi).
For NUMB3RS episode 314 (“Takeout”), we helped to fold many hidden π references into the script review and math notes. The writers, director, cast, and crew added many more. The opening Black Box, for example: a 3-course meal, 1 restaurant, 4 robberies, 1592 death squad murders. Charlie mentions a circle-circle tangency joke not working, right before a James Bond reference (007—circle, circle, tangent).
Below are a few of our π-related Demonstrations. Click on any of them to reach an interactive math demonstration. Enjoy!
February 12, 2008 — Eric Weisstein, Senior Researcher
While MathWorld continues to be the most popular and most visited mathematics site on the internet, and while its mathematical content continues to steadily grow and expand, MathWorld readers will today notice more immediate visual changes.
Design changes and major new pieces of functionality are generally years in the making for large informational websites like MathWorld. The last time the site received a major infrastructure upgrade was in July of 2005 (see “MathWorld Introduces New Interactive Features for Teachers and Students,” MathWorld headline news, July 6, 2005).
On February 8, we introduced a major update of the MathWorld site featuring improved navigation, higher-quality typesetting, and links to interactive Demonstrations.
The new features introduced on MathWorld include:
- New streamlined “platformed” look and feel
- New interactive Demonstration collections and links
- Improved mathematical typesetting
- Collapsible navigation link trails
- More-prominent ways to contribute to MathWorld
Each of these elements is described in more detail below.
January 19, 2008 — Oleksandr Pavlyk, Kernel Technology
Most calculus students might think that if one could compute indefinite integrals, it would always be easy to compute definite ones. After all, they might think, the Fundamental Theorem of Calculus says that one just has to subtract the values of the indefinite integral at the end points to get the definite integral.
So how come inside Mathematica there are thousands of pages of code devoted to working out definite integrals–beyond just subtracting indefinite ones?
The answer, as is often the case, is that in the real world of mathematical computation, things are more complicated than one learns in basic mathematics courses. And to get the correct answer one needs to be considerably more sophisticated.
In a simple case, subtracting indefinite integrals works just fine.
Consider computing the area under a sine curve, which equals
September 25, 2007 — Mark Sofroniou, Kernel Technology
Today we were reminded again about how hard it can be. A nasty little bug in Excel 2007 came to light, whereby the result of computing, for example, 850*77.1 is displayed as 100000:
Of course, this works just fine in Mathematica:
But why is arithmetic so difficult to get right?
August 5, 2007 — Yifan Hu, Kernel Technology
I work on computational algorithms for Mathematica, and I always like to see that what I do is helpful in solving real-world problems.
When I heard about the I-35W bridge collapse, I wanted to see if anything could be learned from computing the mechanics of the bridge with Mathematica.
Large packages have been written for doing structural computations with Mathematica. But I wanted to start from first principles to try to understand the whole picture.
A truss bridge can be thought of as a graph, with trusses as edges and joints as nodes, as in the picture below: