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Celebrate with a slice of pi
Pete Wilton | 13 Mar 09
Did you know that the origins of the number pi can be traced back at least as far as ancient Egypt?
This mathematically magical number defines the ratio of the circumference of a circle to its diameter and, as Marcus du Sautoy describes in a special Inside Oxford Science podcast celebrating Pi Day (14 March), one of the very first recorded estimates of its value appears in the Egyptian Rhind Papyrus.
Marcus tells us that this papyrus, now housed in the British Museum, ‘is full of fantastic mathematics including ideas of how to use binary numbers to do multiplication 3000 years before the German mathematician Leibniz would reveal their potential…’
The papyrus describes how the Egyptian scribe Ahmes attempted to estimate the area of a circular field whose diameter is 9 units across.
Because the area of a circle is pi times the radius squared, if we know the area and we know the radius we can calculate pi. The Rhind papyrus states that a circular field with a diameter of 9 units is equal in area to a square with sides of 8 – but where did this idea come from?
‘My favourite theory sees the answer in the ancient game of Mancala. Mancala boards were very popular during this period and were even found carved on the roofs of temples,’ Marcus reveals.
Here, it’s the Mancala board rather than the game itself that are important as filling the circular holes with stones could inspire pi-tastic thoughts:
‘The player might have gone on to experiment with making larger circles and discovered that 64 stones can be arranged to make a large circle with diameter 9 stones. But 64 stones can also be rearranged into an 8 by 8 square.’
‘By rearranging the stones the circle has been approximated by a square whose area is 64 units. Recall that the area of a circle is pi times the radius squared. The radius in this case is 4 and a half. So Ahmes’s calculation gives the first estimate for pi as the area 64 divided by the radius squared 4.5 squared, which comes out at 256 over 81 or approximately 3.16. Not bad for a first estimate.’
Marcus goes on to explain how the Indian mathematician Aryabhata used a very accurate approximation for pi, (3.1416) to estimate the Earth’s circumference to within an accuracy of 70 miles. And how, in the film Pi, the central character would be just as likely to find the ASCI code for the novel Moby Dick alongside messages from God in the number’s decimal expansion.
What would the value of pi be if we all had fingers like Homer Simpson? You’ll just have to listen and find out…
Lower image: Mancala board by Hanany via Wikimedia Commons.