Original Math Notes
All Seasons
Episode 309: Waste Not--Explore the Math
Original Math Notes
Episode 309: Waste Not
Interactive Computations
Use the free Wolfram Mathematica Player to interact with the math behind NUMB3RS.
Scene 1:
CHARLIE, LARRY and AMITA sip champagne and eyeball the new
Physics-Math-Astronomy (PMA) Chair, DR. MILDRED FRENCH.
She chats with the PROVOST near a microphone.
          
                 PROVOST
          Ladies and Gentlemen...
          
The Provost introduces Dr. French, Charlie whispers to Amita.

                 PROVOST (CONT'D)
          We celebrate the appointment
          of Dr. Mildred French to the
          Physics-Math-Astronomy Chair.
          
                 CHARLIE
          I just want you to know I'm--
          I'm willing to-- to go to bat
          for you with Mildred.
          
                 PROVOST (CONT'D)
          Her work in Algebraic
          Geometry led her to String
          Theory with a strong
          connection to Cosmology-- In
          other words she speaks your
          languages.  All of them.
          
                 AMITA
          Thanks, Charlie.
          
Dr. Mildred French steps to the microphone.

Contours of Algebraic Surfaces

This Demonstration shows zero level sets of various algebraic surfaces and their cutaway views.
Scene 20:
                 CHARLIE
          You're asking about cancer clusters-
          - statistically rare.  More likely,
          it's a case of Texas sharpshooting.
          
                 MEGAN
          Am I about to be mocked?
          
                 CHARLIE
          Say there's a guy who's never held
          a gun before-- he aims at the side
          of a barn and shoots.
          
AUDIENCE VISION.

GUNSHOTS PECK HOLES IN THE SIDE OF AN OLD RED BARN.
CONCENTRIC CIRCLES OF A TARGET ARE THEN DRAWN AROUND THE MAIN
CLUSTER OF SHOTS TO MAKE IT SEEM LIKE THE SHOOTER WAS A
MARKSMAN.  SHOTS ON THE PERIPHERY ARE IGNORED.

                 CHARLIE (V.O.) (CONT'D)
          When he's done, he draws a circle
          around the closest shots, ignores
          the other and declares he's--
          
END AUDIENCE VISION.

                 MEGAN
          A Texas Sharpshooter.

The Bomb Problem

Take a set of random points. In the "Texas sharpshooter problem," the smallest circle that contains three of the points is found. In the "bomb problem," the smallest circle that contains all the points is found.
Scene 36:
Don and Meeks walk with Charlie as a backhoe digs up earth
about fifty yards from the sinkhole.  Agents with shovels and
breathing masks stand by.

                 CHARLIE
          We found Benzene residue in the
          sinkhole.  It's probably what
          killed the elderly lady and caused
          the rashes in the children.
          
                 DON
          Benzene from the aggregate.

Residue Curve Map for a Benzene Toluene P Xylene Mixture

The Demonstration computes the residue curve map for the ternary mixture benzene-toluene-p-xylene. When you change the locator's position, a new residue curve is computed and displayed. Residue curve maps play an important role in the conceptual design of distillation columns.
Scene 37:
     
                 LARRY
          FIRE IN THE HOLE!!!
          
A controlled EXPLOSION!  Everything SHAKES!  Howard jumps.

                 HOWARD MEEKS
          What the hell?!
          
                 CHARLIE
          We're locating the source of the
          acid. Water flows from high to low
          so we know it's in the northeast
          sector above the sinkhole-- but we
          can get a precise location with
          seismic imaging.

Plane Seismic Waves

This Demonstration shows the propagation of elastic waves, commonly known as seismic waves. Two types of seismic waves are shown here: pressure waves (P-waves) and shear waves (S-waves). The P-wave is longitudinal, and so oscillates along the direction of the wave propagation, while the S-wave shakes perpendicular to the travel direction.
 
Wolfram: Creators of Mathematica, Leaders in Math & Computation
Wolfram|Alpha