Last week we reached the stage of drawing the outline of the 'heavenly city diagram' that represents the sphere of earth below the moon. Its main feature is a circle of radius 5,040, the sum of the earth's mean radius, 3,960 miles, and that of the moon, 1,080 miles.

These numbers are all multiples of 12. Number 12 represents structure and order. The Creator is said to have framed the universe in twelves. But to give it life and spirit, he had to include the numbers 5 and 7.

It is easy with compass and ruler to draw a 12-sided figure, but a 7-sided figure is impossible. No one has shown how to construct a heptagon with perfect accuracy. But you can draw it near enough, and one way is to use the framework of the heavenly city. In this diagram the circle accommodates a 28-sided figure. Twelve of its arms go to the" centres of the twelve moon circles, and the others touch their sides.

28 is 4 times 7, and it is also the sum of the numbers 1 to 7. It is the number of lunar mansions in astrology, and the number of days in a lunar month. 7 is the mystical number, symbol of the world-soul that inspires visions and prophecy. Like 7! (7 factorial, i.e. 1x2x3x4x5x6x7) or 5,040, it is the number of the virgin goddess who existed before the creation of the world. She is indefinable, and so is her geometric symbol, the heptagon.

The number 5 represents the last stages in creation, when life and humanity appeared. Its shape, the pentagon, occurs throughout living nature. Roses and many other plant-forms are pentagonal. So is the outline of the human body with its five extremities.

The ratio between the side of a pentagon and its diagonal is 1 to 1.618. . . This is the famous 'golden section' ratio. Scientists have recognised in it the key to natural form and growth. Artists have used it to bring harmony to their compositions. It is displayed in the dimensions of the Great Pyramid. A saying in creative geometry is that the pentagon longs for a mate. By itself, it is sterile and does not grow geometrically. Two pentagons can be married in several ways. One way is to overlap them, producing a 6-sided shape which can then be packed together with others.

With the appearance of plants and animals, the geometer's creation myth comes to its end. It is a good old story, and it provides a gateway into the mysteries of geometry, number and the world itself.

John Michell

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