Original Math Notes
All Seasons
Season 6
Episode 601: Hangman
Assembling an aperiodic tiling
Scene 9:
                  CHARLIE
          Muzzle velocity?
            (off Don)
          Of an... M1A1? 

                  DON
          I dunno -- 7-800 --

                  COLBY
          853 meters per second. Effective 
          range of 460 meters -- 

                  CHARLIE
          Accounts for a roughly --

MORE GUNSHOTS -- one of the SUV windows shatters -- as
Charlie checks his watch as the reports reverberate --

                  CHARLIE (cont'd)
          -- quarter second delay...

Flash Bang Thwack »

You are standing near a target. You see a flash as a gun is fired. Later, you hear the sound of the gun. Finally, you see the target get hit. The delay between these events is determined by the distance of the shooter and the velocity of the bullet. Here, a rifle bullet is used, with a velocity of 150 meters per second. A pistol often has twice that velocity, and an assault rifle four times that speed.
Scene 12:
RESUME Charlie dictating... looking at a PICTURE OF THE
PARTHENON.

                  CHARLIE
          My mother had this photo of the
          Acropolis... from a trip she'd taken
          with my father, before I was born.
            (beat)
          One day, I scribbled all over it with
          a crayon. She was understandably
          upset -- until my Dad pointed out
          that I'd covered it with rectangles
          within rectangles -- retracing the
          Greeks' use of the Golden Ratio.

Golden Spiral »

This Demonstration draws an approximation to a golden spiral using a golden rectangle.
Scene 17:
Larry's PHONE BEEPS -- he reads a text.

                  LARRY (cont'd)
          That's Charlie asking for assistance
          with some aperiodic tiling. You want
          to come with?

                  AMITA
            (pause)
          Actually, I have some low density
          parity check code that isn't writing
          itself.

Robinson Tiling »

Aperiodic tiling showing hierarchical structure, published by Raphael M. Robinson in 1971.
Scene 36:
                  LARRY
          Raspberry seeds are arranged on a
          Fibonacci sequence, aren't they....

Phyllotaxis Spirals in 3D »

In almost all above-ground growth in plants, new sprouts come out at angles of about 137.5° relative to the previous one. But between each sprout, the main stem or trunk has grown different amounts. See the effect this has on the overall form.
 
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