Interactive Computations

Use the free Wolfram *Mathematica Player* to interact with the math
behind NUMB3RS.

CHARLIE packs a duffel with sweatpants, T-shirts and a towel. AMITA watches as he shoves the contents into the bag. AMITA You're making a mess. (grabs it) Let me do it. She folds the T-shirt with perfection. CHARLIE An exact hundred and eighty degree fold, what I'd expect from a master of combinatorics. AMITA Actually, I worked at the Gap in high school.

Fold a piece of paper in half repeatedly and
then unfold the folds uniformly using the same angle. For each angle choice, you get a different fractal curve; these are called dragon curves. The folding is a predictable substitution system, which causes successive
elements to alternate which way they kink out.

CHARLIE Imagine an uncut diamond... MEGAN Not a problem -- ENTER AUDIENCE VISION Of a large, uncut diamond. CHARLIE (V.O.) The diamond is beautiful, but to make it more valuable, you have to cut the diamond perfectly. Zoom into the diamond. CHARLIE (V.O.) (cont'd) Under a microscope, the facets of the diamond are intertwined. We see the fine lines of the diamond connected. CHARLIE (V.O.) (cont'd) In order to get the maximum profit out of the diamond you must cut or untwine the facets. The diamond is cut, falls into four smaller and more brilliant pieces.

Six octahedra are placed at the vertices of a
larger octahedron. The voids within the large octahedron are filled with tetrahedra to form a composite solid
octahedron, which is then placed at the vertices of yet another octahedron, and the voids again are filled with
tetrahedra. This process constitutes two stages of a fractal structure.

Don studies the photo. DON Charlie's helped us find locations based on the shadow of the sun before...

You can use an analog wristwatch to locate the direction of south during daylight hours. It is assumed that you live in
the Northern Hemisphere, not too close to the equator or the North Pole. Hold your watch horizontally and turn it so
that the hour hand points in the direction of the sun. South is then halfway between this direction and twelve o'clock,
which you can mark with the red arrow in this Demonstration.

David plays chess on his computer. Colby next to him. Megan approaches in the background. DAVID Alright, Knight to c3... ON SCREEN - his knight moves. Then, it's the computer's turn. David gets checkmated. YOU LOSE pops up in big letters. DAVID (cont'd) Damn it --

This shows a knight's tour starting from any
position on a chessboard. A classic chess problem is to find a sequence of moves such
that a knight will land on every square exactly once. First position the knight anywhere on the board.

LARRY You know Charles, I'm all for new adventures but the suspense is really starting to get to me. MEGAN This from a man who lived a hundred miles above the earth... LARRY Two hundred twenty-four to be exact.

October 2007 marks the 50th anniversary of the launch of the Russian satellite Sputnik 1, the first human-made object to
orbit the Earth. The satellite was carried into orbit on a Soviet R-7 rocket and had a height of 228 km at perigee
(closest point to Earth) and a height of 945 km at apogee (farthest point from Earth). Its velocity at perigee was 8
km/s and its time for completing one orbit was 96 minutes. Sputnik 1 stayed in orbit for three months before falling to
Earth in January 1958.