Original Math Notes
All Seasons
NUMB3RS Episode 404--Explore the Math
Episode 404: Thirteen
Interactive Computations
Use the free Wolfram Mathematica Player to interact with the math behind NUMB3RS.
Scene 03:
                    LIZ
          Seems like it's not just about the
          numbers.  The elements of the design
          are just as important.

This sparks Charlie, he studies the imagery, the nautilus
shell...

FLASH CHARLIE VISION

Spiralling numbers flowing out of the nautilus shell like
a vivid  natural life force.

BACK TO CHARLIE

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. The arrangement of leaves and petals in plants is known as phyllotaxis. Use this Demonstration to see the effect this has on overall form.
Scene 3:
                    DON
          What is it, Charlie?

                    CHARLIE
          ...It's a Fibonacci sequence. Which
          continues from this first grid here...

Zeckendorf Representation of Integers »

This Demonstration gives the unique representation of positive integers as a sum of nonconsecutive Fibonacci numbers.
Scene 3:
                    DON
          The sequence continues, right?

                    CHARLIE
          Yeah.

                    DON
          So, if there was another grid after
          this one --

                    CHARLIE
          -- The next missing number series
          could be our next victim.

Charlie grabs David's pad, scribbles.  Holds it up.  Another
7-digit number.

Phone Numbers by Fibonacci Methods »

The Fibonacci sequence, 1, 1, 2, 3, 5, 8,..., is obtained by adding the two previous terms to get the next term. By starting with different initial terms, any number can eventually be reached. In this Demonstration, manually chosen phone numbers result at the ends of two different sequences.
Scene 11:
                    ALEX TROWBRIDGE
          What about Fibonacci numbers, the Golden
          Ratio?

                    CHARLIE
          There is evidence that math occurs
          spontaneously in nature and in art.
          And I do acknowledge that there is 
          some mystery to that -- some beauty 
          to that...

Model of Shell Growth »

A simple model for the growth of mollusk shells. In each case new shell material is progressively added at the open end of the shell. The sliders control the amount of material added at each stage at different points around the opening; the line from the center indicates the progressive lateral displacement of the opening. All shells produced by adding material according to fixed rules of the kind shown here have the property that throughout their growth they maintain the same overall shape.
Scene 20:
                    ALEX TROWBRIDGE
          It's called a "gematria" (geh-MAY-
          tria).  People into numerology look
          for meaning in such "digit-sums."

                    CHARLIE
          -- Of course they do.

Gematria (Letter Sums) »

A frequent numerology exercise involves turning letters into numbers (a = 1, b = 2, ..., z = 26), then summing the values (i.e., computing their digits sums). This Demonstration lets you see what words have specific sums.
Scene 20:
A coin-sorting machine.  A BUCKET OF COINS tossed in, as we --

                    AMITA (V.O.)
          Imagine dumping in a bucket-full of
          coins -- not just U.S. coins, but
          currencies from around the world --
          thousands of different coins...

PUSH IN AND DISSOLVE "into" the machine, its inner workings.
The COINS swirl around on a circular tray with different-
sized sorting holes.  EQUATIONS VECTOR-ROTATE WITH THE COINS.

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.
Scene 35:
                    CHARLIE
          If there's a pattern in these last
          four number grids, I don't see it.

                    LARRY
          The repetition of 0's and 1's could
          be some form of binary encoding.

Binary Counting Sequence »

The pattern formed by the binary digits is ultimately nested.
 
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