Science Me

Quick Pix

 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

Why is it hot in the summer and cold in the winter?

Find out in Seasons Reasons in the Science U Observatory.

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

### 5 Minute Seminar:

Isometries: Hollywood does geometry

One way of studying geometry is to think about the sizes and shapes of geometric figures like circles and triangles. Another way is to think about how we can manipulate and transformation such geometric figures. Computer graphics provide an excellent example of why both points of view are important.

Almost all computer graphics are ultimately constructed by drawing points, lines and various polygons, especially triangles. By using many small polygons, the eye perceives the illusion of a smooth object. Indeed, special effects companies like Industrial Light and Magic have elevated making illusions to an art form. However, even the most breathtaking scenes from Jurassic Park still boil down to drawing and moving polygons.

Sometimes, the hardest part of a computer graphics project is figuring out how to draw something. Even though you only have to be able to draw lots of squares, figuring out how to arrange lots of them to even roughly approximate a sphere can be quite a challenge:

Of course, once you have a polygonal model, the temptation to try to animate it is nearly irresistable. Fortunately, unlike creating the model in the first place, where each polygon must be individually positioned, once you understand how to move one polygon on the screen, you can move the entire model by mechanically moving one polygon at a time. It just takes longer.

Next Time: Computer animation basics in "Traveling Triangles".
Complete Seminar Series available in the Science U library.

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