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By Root 726 0

calculator in his teens, when he was taken under the wing of two eminent mathematicians. In the days before electronic or mechanical calculators, scientists relied on logarithm tables to do complicated multiplications and divisions. As I will explain in more detail later, every number has its own logarithm, which can be calculated using a laborious procedure of adding fractions. Dase calculated the natural logarithms of the first 1,005,000 numbers, each to seven decimal places. It took him three years, and he said he enjoyed the task. Then, on the recommendation of the mathematician Carl Friedrich Gauss, Dase embarked on another enormous project: compiling a table of factors of all the numbers between 7,000,000 and 10,000,000. This means he looked at every number in the range and calculated its factors, which are the whole numbers that divide that number. For example, 7,877,433 has only two factors: 3 and 2,625,811. When Dase died, aged 37, he had completed a substantial part of it.

Yet it was another calculation for which Dase is best remembered. When still a teenager he calculated pi to 200 places, a record for the time.

Circles are everywhere in the natural world – you see them in the full moon, in the eyes of humans and animals and in the cross-section of an egg. Tie a dog to a post and the path it patrols when the lead is taut is a circle. The circle is the simplest two-dimensional geometrical shape. An Egyptian farmer counting how much of a crop to plant in a round field, or a Roman mechanic measuring the length of wood for a wheel would have needed to make calculations involving circles.

The ancient civilizations realized that the ratio of a circle’s circumference to its diameter was always the same no matter how big or small you made the circle. (The circumference is the distance around a circle, and the diameter is the distance across it.) The ratio is known as pi, or p, and it works out as just over three. So, if you take the diameter of a circle and curve it around the circumference, you will find that it fits just over three times.

Even though pi is a simple ratio between the basic properties of a circle, the task of finding its exact value has proved to be far from simple. This elusiveness has made pi an object of fascination for thousands of years. It is the only number that is both the name of a song by Kate Bush and a fragrance by Givenchy, whose PR department sent me the following text:

– PI

BEYOND INFINITY

Four thousand years have passed and the mystery remains.

Although every schoolchild studies, the familiar symbol still manages to hide an abyss of great complexity.

Why choose to symbolise the eternal masculine?

It’s a matter of signs and directions. If is the story of the long struggle to achieve the unattainable, it is also a portrait of the fabled conqueror in search of knowledge.

Pi speaks of men, of all men, of their scientific genius, their taste for adventure, their willingness to act, and of their passions to the extreme.

The earliest approximations for pi came from the Babylonians, who used a value of 3 , and the Egyptians, who used 4(, which translate, respectively, into decimals as 3.125 and 3.160. A line in the Bible reveals a situation in which pi is taken as 3: ‘Also he made a molten sea of ten cubits from brim to brim, round in compass, and five cubits the height thereof; and a line of thirty cubits did compass it round about’ (I Kings 7:23).

If the shape of the sea is a circle with a circumference of 30 cubits and a diameter of 10, then pi is , or 3. Many excuses have been given for the Bible’s inaccurate value, such as the claim that the sea was in a circular vessel with a thick rim. In this case the quoted 10-cubit diameter covers the sea and the rim (making the true diameter of the sea a little less than 10 cubits), while the circumference of the sea is taken as the inside of the rim. A mystical explanation is much more enticing: due to the peculiarities of Hebrew pronunciation and spelling, the word ‘line’, or qwh, is pronounced qw. Totting