Interactive Computations

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

CHARLIE Think of a gum ball machine, packed with hundreds of gum balls. And imagine striking it with a sledgehammer...

In the linked Demonstration, use the trigger to animate the simulated projectile. Change the initial conditions by varying the
sliders.

CHARLIE It's the same with this image. It's being scattered by the forces of refraction... But using Snell's Law, a dash of Goos-Haenchen shifts and a motion-tracking algorithm...

Light travels at different speeds through different materials, causing it to bend according to Snell's law. Here light
is represented by traveling wavefronts coming from a light source above the boundary between two materials.

CHARLIE From the picture, we can see that the final water level in the tub was right about here.

Filling a pool requires a lot of water. This Demonstration gives the volume of water contained within many pool
types.

LARRY I did think some of the math was a little subjective... your random Apollonian Networks in particular.

At each step, inscribe new tangent disks
into each open curvilinear triangle.
These open regions fill up quickly, leaving a fractal of infinitely many points that are never in any circle. The resulting figure is known
as the Apollonian gasket.

CHARLIE Part of Game Theory is Risk and Response Analysis.

Often the probability of an accident is
determined by both the behavior of someone who is not injured by the accident in the legal sense and the behavior of
someone who is injured.

CHARLIE The model becomes a predictor. Same way economists predict grain futures or currency markets.

A representative investor trades a single asset using the simplest possible rule and still generates complexity. The investor looks back a fixed
number of days to decide whether to buy or sell.