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The History of Pi?

[ maths ]
asked on 21 Jan 2011
Abigail Silva Abigail Silva
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There is a great deal of interest nowadays in the book, Life of Pi. The concept of Pi has fascinated people through the ages, from unknown Egyptian and Babylonian architects who must first have encountered its challenge to modern mathematicians and scientists aided by supercomputers who have now gauged its value to a trillion decimal places.

Pi simply is the constant, denoted ∏, which when multiplied with the diameter of a circle, will give its circumference. A simple approximation that many of us use is 3.142 but architects, engineers and scientists require a more precise definition and hence the search for a precise answer. Archimedes is known to have estimated the value of Pi by applying the common sense logic that a circle must be bounded internally and externally by a regular polygon of large enough number of sides. He is said to have calculated the dimension of a 96 sided polygon that bounded a circle and thereafter gave up attempting any more precise a definition of the elusive Pi.

We now know that Pi is an irrational number, which means that it cannot be expressed as a ratio of any two integers. There is archaeological evidence that the ancient Egyptians knew something about this fraction, and were taken up enough by its unfathomable nature, that they enshrined it in their monuments. The Great Pyramid at Giza constructed in 2500 BC, was built with a perimeter of 1760 cubits and a height of 280 cubits which gives a ratio equivalent to 2 ∏. It cannot be pure chance that this great monument was built to this ratio. The equivalent value of ∏ in this ratio comes to be 3 + 1/7 or 22/7 which is what students in schools still commonly use in its place.

Around 1400 AD, an Indian, Madhava of Sangamagrama estimated Pi to eleven decimal places by equating Pi to an infinite series. The development of infinite series to estimate mathematical values was a great innovation that helped achieve greater precision in calculations. Srinivasa Ramanujam is known to have expressed Pi in the form of several such series, each of them giving another way of reaching closer to the value of Pi.

A German, Ludolph van Ceulen, devoted the greater part of his life to estimating the value of Pi, and he managed to solve value Pi to 35 decimal places using geometrical methods in the sixteenth century. He was so proud of his achievement, that he had these decimals inscribed on his tombstone. Ever since, the constant is often known as Ludolph’s Constant. It is also better known as Archimedes’ Constant.

It was only afterwards, in the 18th century that the nature of Pi was understood as irrational, and it took another century to understand that it is a transcendental number, which means that there is no polynomial with rational coefficients for which Pi is the root. That simply means that Pi is not constructible with compass and straight edge.

Teachers of mathematics have naturally tended to use Pi, as a symbol for mathematical enquiry. March 14 is celebrated as Pi Day in some parts of the world. The date relates closely to 3.14 which is an approximation of the value of Pi. Schools and colleges take the opportunity to hold competitions and displays related to maths on this day. A popular contest is often around how many digits of Pi can be memorised and retold accurately. People have managed to recite over 10000 digits from memory.

There are many websites dedicated to Pi, and its teaching. We have even come across verses and lyrics composed around the inscrutable Pi. Here is one from a website dedicated to the teaching of Pi:

“Oh, number Pi, Oh, number Pi You’re truly transcendental. Oh, number Pi, Oh, number Pi You’re physical and mental. You stretch the bounds…of all we know, And tell our circles where to go Oh, number Pi…..”

answered on 21 Jan 2011
Joe Seb Joe Seb
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