Ed Pegg Jr., May 1, 2007
Mathematica 6 has just been released. It's a great program, but I'm an employee of Wolfram Research. I'm reminded of when I saw Penn, of Penn and Teller, juggling three large freshly broken bottles. One of the bottles had a truly ghastly curved spiralling jagged shard. "That's a very nasty looking bottle there!" exclaimed Penn, whirling the particular one in front of his face. "That's just part of my normal patter for this act. I always say how nasty the bottles look. But this time, I'm really serious." I believed him. So now, as a biased employee, I'm now engaged in predictable patter, trying to lure you into going to the Mathematica 6 launch page. It has an amazing flash banner. And this time, I'm really serious. A small part of the Mathematica 6 launch is the Wolfram Demonstrations Project.
Figure 1: Twelve of the 1200+ available math demostrations.
The Wolfram Demonstrations Project demonstrates over a thousand mathematical concepts, with more being added every day. Most amazingly, these interactive demonstrations are available free, and can be used by anyone. All you need is the Mathematica Player (also free). There is a wide selection of mathematics on display, and anyone may contribute more.
For example, a calculation can find the scrap metal price of coins. The US Jefferson Nickel is particularly interesting right now -- $1.00 worth of normal nickels has a scrap metal price of $1.88 (as of 1 May, 2007). That's mainly because the metal nickel is near an all time high. With this demonstration, the sliders can be moved to give the current spot price of each metal, and the price of the coins is either the scrap metal price, or $1, whichever is greater. As a sidenote, it's now illegal to melt US Coins.
Figure 2: The Scrap Metal price of Coins.
Tobias Kreisel and Sascha Kurz found an Integer Distance Heptagon -- a set of seven points, no three on a line and no four on a circle, so that all points are at integer distances from each other. I wanted to make a nice picture of this, and a bit of interactivity helped for instantly labeling all the lines. The existance of an integer heptagon was been a long-unsolved question. Is there an integer octagon?
Figure 3. Labeling the Integer Heptagon.
If you want a statue to look as big as possible, where should you stand? If you are too close, the statue will be foreshortened. If far away, the statue will appear small. In the fourteenth century, Johannes Regiomontanus solved this question. It's a nice geometry problem.
Figure 4. The Statue of Regiomontanus.
Many educational demonstrations are available. For example, the slope-intersect formulas for lines, shown below. This demo is by Abby Brown, of abbymath.com. Abby made many educational demonstrations for her classes, such as conic section curves, projectile motion, illustrating cosine with the unit circle, and solids of revolution.
Figure 5. Lines: Slope-Intercept, by Abby Brown.
Various interactive tables of mathematical data are included. For example, the ever popular table of prime factorizations. Demonstrations are available for factoring binomials, how Pratt certificates of primality work, LU decomposition, singular value decomposition, polynomial long multiplication, polynomial long division, and much more.
Figure 6. Prime Factorization Table.
An interactive slide rule is available, by George Beck (calc101.com). The slide rule really works, with moving bars. If you need some brush-up on how slide rules work, you can visit multiplication by adding logs, or logplots and beyond.
Figure 7. Slide Rule, by George Beck.
Many interactive puzzles are available. For example, each of the dots within the Orchard Planting Problem can be moved around on the grid.
George Hart, "4D Polytopes and 3D Models of Them," http://www.cs.sunysb.edu/~cse125/notes/08-4D-Forms.ppt.
George Hart, "4D Polytope Projection Models by 3D Printing," May 3, 2002. http://www.georgehart.com/hyperspace/hart-120-cell.html.
Paul Hildebrandt, "Zome-inspired Sculpture," http://www.lkl.ac.uk/bridges/Zome-Hildebrandt.pdf.
Roice Nelson, "Explore the 120-Cell," July 1, 2006. http://www.gravitation3d.com/120cell/.
Mark Newbold, "Hyperspace Star Polytope Slicer," Feb 1, 2003. http://www.dogfeathers.com/java/hyperstar.html.
Fritz Obermeyer, "Jenn 3d," http://www.math.cmu.edu/~fho/jenn/.
Marc Pelletier, "Paul Donchian, Modeler of Higher Dimensions," Fields Institute Presentation, February 15, 2002. http://www.fields.utoronto.ca/audio/01-02/sculpture/pelletier/.
Ivars Petersen, "Math Trek: Quark Park," Nov 11, 2006. http://www.sciencenews.org/articles/20061111/mathtrek.asp.
Miodrag Sremcevic, Radmila Sazdanovic, and Srdjan Vukmirovic, "Tessellations of the Euclidean, Elliptic and Hyperbolic Plane," Wolfram Information Center, March 23, 2003. http://library.wolfram.com/infocenter/MathSource/4540/.
John Stillwell, "The Story of the 120-Cell," Notices of the AMS, Jan 2001. http://www.ams.org/notices/200101/fea-stillwell.pdf.
Jeff Weeks, Curved Spaces 3, Dec 2006. http://www.geometrygames.org/CurvedSpaces/.
Andrew Weimholt, "120-Cell Foldout," http://www.weimholt.com/andrew/120.html.
Comments are welcome. Please send comments to Ed Pegg Jr. at email@example.com.
Ed Pegg Jr. is the webmaster of mathpuzzle.com. He works at Wolfram Research, Inc. as an associate editor of MathWorld. He is also a math consultant for the TV show Numb3rs.