Original Math Notes
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Season 5: Are You a math genius? Can you solve this weeks puzzle?
Season 5
Episode 501: High Exposure
Wave-particle duality visualized: Forming a superposition of plane waves that results in a coherent state concentrated along the trajectory of an elastic sphere on a square two-dimensional billiard table
Interactive Computations
Use the free Wolfram Mathematica Player to interact with the math behind NUMB3RS.
Scene 10:
Amita holds the diamond up to the light.


ENTER AUDIENCE VISION:

The diamond transforms into a CUT DIAMOND, sparkling.

                    AMITA (cont'd)
          A diamond is a crystal, its atoms
          arranged in a symmetrical
          structure.

ZOOM INSIDE THE DIAMOND -- revealing the crystalline
structure of the carbon atoms -- creating regular cubes.

                    AMITA (cont'd)
          Optic crystallographic analysis
          shines a polarized light from an
          electron microscope into the
          crystal structure --

RAYS OF LIGHT blast through the CRYSTALLINE STRUCTURE and
break off at thousands of angles as they collide with atoms.

Lattices in Perspective »

This Demonstration shows a perspective rendering of disks or spheres in a cubic lattice. In order to view the rendering correctly, the eye should be directly above the center of the image, exactly one half of the width of the window away from the screen. Interestingly, the image with circles really is a perspective image of disks in space; when viewed from the correct vantage point, these are squashed into ellipses. On the other hand, spheres are drawn as elongated ellipses that appear to be perfectly circular when viewed correctly.
Scene 66:
Larry studies an enlarged image of the listening device on a
screen.  Amita studies the real thing through an evidence bag.

                    AMITA
          To get past the electronic shield
          that was installed in the store,
          this device was wired to a small
          satellite dish on the roof.  That
          way it sends a signal to a
          satellite, which in turn relays it
          to a receiver on the ground.

Geosynchronous Orbit »

The Clarke Belt represents the position over the equator where an orbiting satellite will remain in a fixed position over the Earth, 22,300 miles (35,786 km) up. Arthur Clarke suggested the usefulness of geosynchronous orbits in 1945.
Scene 68:
                    LARRY
          No, it's not the case.  I've got a
          vector problem tracking an
          unidentified subatomic particle
          across a complex energy field.

Energy Density of a Particle Moving at Uniform Speed »

The four components of the potential of a point charge are used to compute various electric and magnetic properties. The system is rotationally symmetric. The charge enters the observation plane, passes the origin with positive speed, then leaves the observation plane. The electric and magnetic field vectors, the Poynting vector, and the energy density are displayed on the observation plane.
Scene 79:
Ian chuckles.  Larry lines up a shot, evaluating the angles.

                    LARRY
          Particle physicists like to use
          pool balls to describe the actions
          of sub-atomic elements -- but I can
          assure you that these massive
          spheres behave in a far more
          predictable, Newtonian manner.
          Now, if this cue ball had the
          characteristics of a boson --

Pool Shot »

Shoot a pool ball in the unit square.
 
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