Interactive Computations

Use the free Wolfram *Mathematica Player* to interact with the math
behind NUMB3RS.

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

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.

DON What is it, Charlie? CHARLIE ...It's a Fibonacci sequence. Which continues from this first grid here...

This Demonstration gives the unique representation of positive integers as a sum of nonconsecutive Fibonacci numbers.

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.

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.

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...

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.

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.

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.

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 --thousandsof 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.

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 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.