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Quick Pix

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 It is easy to fill a cube up with smaller cubes, but in Euclidean geometry, dodecahedra don't fit together so nicely. However, it is still possible if you allow yourself infinitely many smaller and smaller dodecahedra. This picture, created by Chiam Goodman-Strauss and Dan Krech, shows one step in the procedure.

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

 Visit the famous curve index and learn about dozens figures such as the Lemniscate of Bernoulli shown here. The curve index is just part of the extensive History of Mathematics site at the University of St. Andrews. Other main attractions include:

Five-Minute Seminar
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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.

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