With a click of the mouse, you can explore the visual landscape of the math
behind NUMB3RS. You'll be running the same programs that the Wolfram
NUMB3RS team uses. See what you can discover!
BRETT
Hey, Spielberg, you might wanna
take the lens cap off.
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.
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.
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.
Use the free Wolfram Mathematica Player to interact with the math
behind NUMB3RS.
