   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.
```

# Projectile Motion » 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.
```

# Wavefunctions of Identical Particles » 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.
```

# Radial 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.
```

# Rolling Disk » 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-
```

# Orbital Elements » Use this Demonstration to explore the five parameters which characterize orbits about a central mass.  ```                    CHARLIE
It's a phenomenon related to
centripetal force --
```

# Rhombic Drive for Speed Governor » 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.
```

# Circumference of a Circle » 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.
```

# Orbits Around and Through a Sphere » 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."
```

# Bingo Card Generator » 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.   