Archive for Thursday 10th July 2003 - The Secret Numbers at the Heart of Creation

Right-angle triangles with whole-number sides are called Pythagorean. The first is the triangle with sides of 3, 4 and 5. Eight of them form a square 7 by 7, leaving a central blank square 1 by 1.

Creative geometry is very simple. You only have to know Pythagoras's theorem and a few tricks of the trade, and soon you will be able to construct the traditional plan of the universe.

Pythagoras was a Greek from Samos in the sixth century BC. He travelled to Egypt and other centres of learning, studying the science and philosophy behind ancient civilisations. He then expressed that knowledge in mathematical form, and taught it through music and geometry. From his famous theorem, we discover the other important ratios of 'sacred' or 'creative' geometry.

If the side of a square measures 1, the length of its diagonal is the square root of 2. If the side of a rhombus (two equilateral triangles back to back) is 1, its long axis is the square root of 3. These ratios occur all the time in the constructions of creative geometry. But they are not the most important. Above them is the primary relationship, between the diameter of a circle and its circumference. That ratio is known by the Greek letter pi. If you multiply the diameter by pi you get the circumference. But what exactly is the value of pi? There is the catch, because it turns out that pi is 'irrational'. It cannot be expressed as a ratio between two whole numbers. It is 3.141592. . . going on forever. And it is the same with other important ratios in geometry. They too are irrational. This means we cannot hope to make a perfect plan of the universe, rationally and in whole numbers. We have to use close approximations to the ratios. For pi we use 22/7 or 864/275; for the square root of 2, 99/70 and for the square root of 3, 71/41.

Next week, I will show you why these ratios were so important to the ancients, who saw them as the signature of a benevolent Creator who used the same basic rules of geometry, over and over again. Then, we shall attempt to understand how the world was really made.

PYTHAGORAS THE MYSTIC WITH A TERRIBLE SECRET
Pythagoras was no ordinary mathematician. He saw his work as a way of getting to the mind of the creator. He led a special cult which you could join only if you swore to become celibate and vegetarian. Members would be shown the secret of the "Prime Numbers" - which are divisible only by themselves. To reveal these to a non-initiate was a crime punishable by death! Yet all we remember him for today is his famous theorem. This applies only to right-angle triangles. It states that "the square on the hypotenuse is equal to the sum of the squares on the other two sides". The hypotenuse is the longest side of the triangle, opposite the right angle. If you draw a square upon it, and squares upon the two smaller sides, the area of the largest square will equal the area of the two others combined.

John Michell

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