Science Me

Quick Pix

 In the strange world of 3-dimensional hyperbolic space, dodecahedra fit together perfectly to completely fill up space as shown here. This image is a scene from the award winning video Not Knot".

Today at Science U

Make a Jupiter Movie!

Or choose another planet if you prefer. On the Orrery Movie Page you're the director.

Focus on Math

What is the next term in the sequence:
 2, 3, 3, 5, 10, 13, 39, 43, 172, 177, ...
 1, 3, 7, 12, 18, 26, 35, 45, 56, 69, 83, ...
Give up? You can find the answer to these, and virtually any other integer sequence problem, at Sloane's On-Line Encyclopedia of Integer Sequences. With over 38,000 sequences catalogue in this vast and intriguing database, you can torment your favorite puzzler with a new sequence every day for the next hundred years -- provided you keep a lid on the URL.

Five-Minute Seminar
Introduction to Isometries: Teapots and Triangles

What do teapots and triangles have in common? If you said "nothing" you must have something against the letter "t". However, the correct answer for the day is that computer animations of teapots and triangles both boil down to the same basic geometric transformations, called isometries.

One way of looking at geometry is to think about shapes and sizes. Triangle, circles, cones, and so on, come up again and again in science, industry and commerce. When most of us first encounter geometry, we learn formulas and theorems describing useful and interesting properties of these shapes. Indeed, it was probably the need to compute weights and volumes that led merchants and traders to think about geometry formulas nearly 3000 years ago, and elaborating the study of shapes and sizes dominated geometers for the next several millenia.

However, starting in the 19th century, another way of looking at geometry emerged. The idea was to focus on how to manipulate and transform geometric objects instead of focusing on the objects themselves. This proved to be very effective, and rapidly lead to discoveries about non-Euclidean geometries, the theory of relativity, and even computer graphics.

Next Time: a closer look at computer graphics in "Geometry goes to Hollywood".
Complete Seminar Series available in the Science U Library.

 Info Center | Geometry Center | Library | Observatory | Studio | Store | Science Me Copyright © Geometry Technologies 1998. All right reserved.