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Fibonacci numbers

Can you see the pattern in this series of numbers?

1, 1, 2, 3, 5, 8, 13, . . .

What is the next number in the series?

Start of the spiral of Fibonacci numbers

Think about this before scrolling down the page to read on. Look at the diagram above: it will become clear.

. . . . .

Let us now shrink the diagram above, and put it in the middle of the next diagram. The spiral continues outwards . . .

The spiral of numbers continues

We now replace the numbers by shapes, as nature does, to create a snail shell. Pythagoras said, All is number.


Fibonacci spiral

The snail must grow in such a way that its body remains more or less the same size in relation to its shell, otherwise the shell would become too heavy to drag around. Also the snail has to fit its body into the big end of the shell. Thus the most recent addition to the shell will maintain a more or less constant relationship with all the shell that has gone before. In an analogous way, each number in the Fibonacci series is the sum of the previous two numbers, and the side of each square in our diagrams is the sum of the sides of the previous two squares.

The relationship between any number in the Fibonacci series and the one immediately preceding it can be expressed as a ratio, which you can work out as a decimal on a calculator. Thus we have 1/1, 2/1, 3/2, 5/3, 8/5 ... etc. (for example, 5/3=1.666..., and 8/5=1.6). If you work them out, you will find that these ratios jump back and forth on either side of a hidden number, getting closer and closer to it.

The hidden number is called the Golden Ratio or phi:

According to Leonardo's theory of human proportion, the height of an adult human being in relation to the height of his umbilicus from the ground is equal to phi).

According to my theory, it is also the case that the length of the trunk, as measured from the chin to the middle of the pubic bone, is 1/phi in relation to the remainder (legs and head) added together, or in other words, 1/(phi^2) in relation to the total height. 1/(phi^2) approximates to 3/8, two numbers belonging to the Fibonacci series. This follows from Leonardo's diagram of the adult male, but my contention is that this rule of proportion is applicable to all ages.

To Human Proportions I

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