Original Math Notes
All Seasons
Episode 414: Checkmate--Explore the Math
Original Math Notes
Episode 414: Checkmate
Interactive Computations
Use the free Wolfram Mathematica Player to interact with the math behind NUMB3RS.
Scene 4:
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.

Paperfolding Dragon Curve

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.
Scene 15:
                   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.

Octahedron Fractal »

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.
Scene 22:
Don studies the photo.

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

Wristwatch as a Compass

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.
Scene 26:
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 --

The Knight's Tour

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.
Scene 64:
                   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.

Sputnik 1 Orbiting the Earth

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.
 
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