Wednesday, March 20, 2002 :::
Enjoy the exam question with the cube and the dodecahedron? Well, party on with this java applet and see it from any angle or watch it spin... But why stop there? The links on the left of the page let you replace that cube with a tetrahedron or octahedron, hey you name it. But wait there's more! Tired of the dodecahedron? Try putting that cube of yours in an octahedron or an isosahedron... and more! A neat example of our work and computer graphics ; )
::: posted by A. at 1:40 PM
Thursday, February 28, 2002 :::
Here's a mathematica notebook that quickly does some parametric plotting of curves and a few other things: geomClass.nb.
::: posted by Angela at 2:37 PM
Roulettes A-Go-Go! Here that favorite childhood toy the spirograph, all fancified on the computer. One of the nice things about this spirograph is that it gives you the parametric equations used to draw the curve!
For another spirograph, download this Mathematica notebook: spirograph.nb from the Mathematica site. You need Mathematica or math reader to use it.
::: posted by Angela at 2:12 PM
Monday, February 25, 2002 :::
Everyone knows that the cycloid is the solution to the brachistochone and tautochone problems, but did you know that in 1673, Christiaan Huygens used this fact to improve his already impressive pendulum clock?
Pendulum clocks are great, but the period of a pendulum varies with amplitude, leaving you confused and grouchy. But because of the amazing properties of the cycloid, Huygens was able to fix this discrepency by wedging the rod of the pendulum between two cycloidial cheeks! Catch all the action at this website. Cycloids are also used to construct half pipes for skateboarders, further proving that you can't escape math, even on wheels.
::: posted by A. at 12:59 AM
Thursday, February 07, 2002 :::
Here's some links having to do with inversion in circles:
- Apollonius of Perga was in some sense the first to discover inversion in a circle (although he certainly didn't call it that!). His problem is outlined in section 6.6 if you want to read it.
- Here's a java animation of a tangent pencil of coaxal circles. The circle traced out in yellow is a member of the orthogonal pencil.
- Here's a nice collection of pages with drawings and animations on circle inversion.
- If we take a collection of circles and follow a point and we repeated invert it in a randomly chosen circle, the limit points often form fractal images! Here's an explanation, which contains some nice pictures and animations, such as this.
- Also, there's several nice pages on mathworld such as the page on Steiner's Porism and this page on coaxal circles.
::: posted by Angela at 5:37 PM
Thursday, January 31, 2002 :::
This shows what you get by being a member of the MAA -- I just got this month's issue of Focus and it mentioned a web site with all of Euclid's Elements presented complete with java programs that illustrate the ideas. You probably want to read the directions on how to use the java applet before getting started. Be forewarned that it can take a while to load. The java applets can really help you to see what the heck the propositions are about, and the propositions are all proven in a clear fashion. What a find!
::: posted by A. at 6:44 PM
Monday, January 28, 2002 :::
Math Jokes!!
Whats purple and commutes? An abelian grape.
What do you say when you see an empty parrot cage? Polygon.
There are many, many more.
you can thank me later :D
melissa
::: posted by A. at 8:33 PM
This shows what you get by being a member of the MAA -- I just got this month's issue of Focus and it mentioned a web site with all of Euclid's Elements presented complete with java programs that illustrate the ideas. You probably want to read the directions on how to use the java applet before getting started. Be forewarned that it can take a while to load. The java applets can really help you to see what the heck the propositions are about, and the propositions are all proven in a clear fashion. What a find!
::: posted by A. at 4:33 PM
Most of you probably know about these sites, but they're a good waste of time. Mathworld is a good general reference. It's run/funded by the Mathematica people and was shut down for over a year due to copyright problems. But now it's back to being useful and free. Biographies of many people math related. Shows relations and how people were influenced.
::: posted by A. at 11:58 AM
Thursday, January 24, 2002 :::
Some information about tessellations can be found here at the math forum .
::: posted by A. at 5:16 PM
Wednesday, January 23, 2002 :::
This is a little java applet that I stole off of the Java Sketchpad page. Its a tesselation of the plane that you can play with by dragging the red points with the mouse. Perhaps someone can make some Sketchpad images or scripts to share with the class!
::: posted by Angela at 8:12 PM
The snowflake at the top of the page was photographed by Wilson Bentley.
::: posted by Angela at 4:57 PM
Wallpaper Patterns
For information about the wallpaper groups and wallpaper patterns (that is, symmetry groups of the plane, as discussed in class), see David Joyce's Wallpaper Groups
For a great Java program that lets you play with your own wallpaper patterns on line, go to the Java Kali Home Page
For Japanese wallpaper patterns, try: Seventeen Kinds of Wallpaper Patterns
::: posted by Angela at 4:53 PM
