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Episode 403: Hollywood Homicide--Explore the Math
Episode 403: Hollywood Homicide
Interactive Computations
Use the free Wolfram Mathematica Player to interact with the math behind NUMB3RS.
Scene 1:
         Hey, Spielberg, you might wanna
         take the lens cap off.

Designing Optical Systems »

This demonstrates an interactive lens system. Download the linked Demonstration, then move any of the blue dots to control the location, thickness, and curvature of the lenses, or the starting point or angle of the rays.
Scene 5:
         Think of a gum ball machine,
         packed with hundreds of gum balls.
         And imagine striking it with a

Animated Projectile Motion »

In the linked Demonstration, use the trigger to animate the simulated projectile. Change the initial conditions by varying the sliders.
Scene 5:
         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...

Snell's Law of Refraction (Wavefronts) »

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.
Scene 19:
         From the picture, we can see that
         the final water level in the tub
         was right about here.

How Many Gallons in My Pool? »

Filling a pool requires a lot of water. This Demonstration gives the volume of water contained within many pool types.
Scene 22:
         I did think some of the math was
         a little subjective... your random
         Apollonian Networks in particular.

Apollonian Gasket »

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.
Scene 39:
         Part of Game Theory is Risk and
         Response Analysis.

Bilateral Accident Model »

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.
Scene 41:
         The model becomes a predictor.
         Same way economists predict grain
         futures or currency markets.

The Minimal Model of the Complexity of Financial Security Prices »

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.
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