Two, Three and Five

Why Are The Numbers

2, 3 and 5 So Important?

1. -by Paul Hildebrandt

   

   
   

Most human activity on the planet today is accounted for in zeros and ones. Which means that the concepts of 2, 3 and 5 are higher math for most adult human beings.

But you can actually generate the numbers 2, 3  and 5 from 0 and 1:

0+1=1

   1+1=2

     1+2=3

       2+3=5

         3+5=8...

This is called the Fibonacci sequence. These numbers are used by nature all the time. for example, members of the mint family (like basil) sprout leaves with 2-fold reflection symmetry in pairs of 2, in 2 directions mutually perpendicular to the stem. The Ichiban eggplant has spirals of 2 leaves in one direction and 3 leaves in the other. The rose has spirals of 3 petals in one direction and 5 petals in the other.

A pine cone has 3+5=8 spirals in one direction and 5+8=13 spirals in the other. A strawberry has spirals of seeds: 8+13=21 in one direction and 13+21=34 in the other. And a sunflower has 21+34=55 spirals of seeds in one direction and 34+55+89 in the other. The ratio of 55:34 is the Golden Section, to the nearest 1/1000. In other words, Fibonacci numbers are a rational approximation of the Golden Section. The Golden Section is an irrational number, a concept which can only exist in the mind. Nature can't do irrational numbers ("yeah, even the hairs on your head are numbered"), so it uses 2, 3 and 5 to approximate.

But why should nature use Fibonnacci numbers? I believe it is the most natural way to grow. In life's simplest forms, growth is based on cell division, i.e. from 1:2. But this kind of growth can quickly get out of control (1,2,4,8,16,32...) like cancer. Nature asks, "what numbers should I use so that new growth is proportional to old growth in the same way that old growth is proportional to the whole plant?" And she finds the answer in the Golden Section as approximated by Fibonacci numbers.

2, 3, and 5 are the first 3 prime factors. This means they appear in the natural (as seen above) and the built world all the time:

A square is a 2-dimensional number 4: 4=2x2

A hexagon is a 2-dimensional number 6: 6=2x3

A decagon is a 2-dimensional number 10: 10=2x5

The tetrahedron has 2x2=4 faces, 2x2=4 corners and 2x3=6 edges.

The cube has 2x3=6 faces, 2x2x2=8 corners and 2x2x3=12 edges.

The octahedron has 2x2x2=8 faces, 2x3=6 corners and 2x2x3=12 edges. Note that the cube and octahedron are duals, which means they have the same number of edges, and the number of faces on the cube equals the number of corners on the octahedron, and vice versa (the tetrahedron is a "self-dual").

The icosahedron has 2x2x5=20 faces, 2x2x3=12 corners and 2x3x5=30 edges.

The dodecahedron has 2x2x2 faces, 2x2x5=20 corners and 2x3x5=30 edges. The icosahedron and dodecahedron are also duals, which means they have the same number of edges, and the number of faces on the icosahedron equals the number of corners on the dodecahedron, and vice versa.

These relationships weren't lost on the ancient Babylonians who invented the 2x2x3x5=60 minute hour, the 2x2x2x3=24 hour day, and the 2x2x2x3x3x5=360 degree circle (note three 2s, two 3s and one 5!). The reason for using the first 3 prime factors to generate these numbers is logical: it maximizes possible whole number divisions. For example, a 60-minute hour can be evenly divided by 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30.