Interactive Computations

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

DON A car made of stolen parts from around the country drives straight into a coffee shop. CHARLIE The CHP accident analysis will tell you how it happened. DON But I want to know why. CHARLIE That's tricky -- finding motive in skid marks and trajectories.

The Moon has less gravity than the Earth, so a dropped or thrown object takes longer to land. In this Demonstration,
the times and trajectories of hurled objects are plotted for various planets.

AMITA I see you're reading Dr. Preskill's paper on quantum particles and multi-dimensionality.

Explore the quantum mechanical probability density for two particles in a one-dimensional square well with infinite walls.

Galinski goes to a computer, punches up a screen. Detailed computer graphic of a Mars Rover, then a car, then a truck -- GALINSKI My own computer modeling software -- analyzes anything with an engine.

This Demonstration shows a working model of a four-stroke radial engine. Unlike a straight cylinder engine, the
cylinders are connected to the crankshaft via a single hub with a master-and-articulating-rods assembly. This engine
configuration was very popular in WWII aircraft. For smooth firing order, most four-stroke radial engines have an odd
number of cylinders.

GALINSKI Mechanical engineering -- the poetry of matter and energy, of metal and power. The more complicated it is, the more beautiful it becomes. CHARLIE We need to know if a certain vehicle's trajectory was accidental or intended.

This Demonstration shows snapshots of a disk rolling on a plane. For the calculation, it is assumed that the disk has
infinitesimal thickness, rolls without friction, and does not slide or slip. A rolling disk is one of the simplest
examples of a nonholonomic system. It
is completely integrable, and as a result,
the sequence of snapshots form nonchaotic
sequences exhibiting a certain symmetry.

CHARLIE Computer simulations are mathematical representations of the real world. Think of Newton -- Newton observed a real world event- The APPLE falls from the tree. And he created a mathematical model to represent the phenomenon- That model could be extrapolated to predict the orbits of planets-

Use this Demonstration to explore the five parameters which characterize orbits about a central mass.

CHARLIE It's a phenomenon related to centripetal force --

Four rods are attached to each other with hinges at the vertices of a rhombus. Two of the sides are extended, with balls
attached at their ends. The top vertex has a constant height. As you rotate the whole assembly, the balls move upward
due to centripetal force.

CHARLIE The further from the center of the circle, the greater the distance traveled.

The circumference of a
unit circle is 2π, or about 6.28.

The APPLE stops mid-air. GRAPHIC overlay displays Newton's equations of motion and the law of universal gravitation. CHARLIE (O.S.) (cont'd) That model could be extrapolated to predict the orbits of planets- The SOLAR SYSTEM -- planets in motion around the sun.

This Demonstration shows the orbit of a test mass in the gravitational field of a homogeneous sphere. Assume that the
test mass can penetrate the sphere without frictional forces being exerted. Inside the sphere, the gravitational force
forms a harmonic oscillator and outside the sphere, it has a pure Coulomb potential. In both cases, the orbits are ellipses. In case the orbit has segments both
inside and outside the sphere, rosette orbits are obtained.

GALINSKI And that, folks, is geek speak for "bingo."

In the game of Bingo, players must be the first to meet various spot-filling criteria: a row, column, or diagonal; a
"T"; an "H"; all spots filled, etc. The most common game is to be the first to fill five spots in a
straight line.