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Name: gordon t davis  joseph f  and  strountree
Status: N/A
Age: N/A
Location: N/A
Country: N/A
Date: Around 1995


Question:
Why is a circle divided into 360 degrees?
From where did the name pi come?


Replies:
The ancient greeks decided (probably based on experiments: try using a cord to estimate the circumference of some cylinders) that the perimeter of a circle (and other symmetric objects) must be a constant multiple of its diameter. A little later attempts were made to estimate the value of the constant using the geometry of inscribed polygons. Much later, when symbolism became more popular in mathematics, "pi" (the first letter in the greek word for perimeter) started to gain acceptance for representing this famous constant. Full details on how "they" get it are too long to type here. Perhaps the earliest estimate for PI was 3. I believe that Archime- des gets credit for using geometry to improve the estimate to 22/7. The greeks at that time loved pure fractions and used nothing like our many decimal representations. Your calculator shows that 22/7 is about 3.142856 or 3.14 rounded to 2 decimal places. Records show that an even better estimate of 355/113 = 3.1415929 was known to ancient chinese mathemati- cians. Using computers, estimates for Pi are now correctly known to millions of decimal places. Look up Wallis' formula for more unusual ways to write fractions, etc. to Pi.

The origins of 360 degree units around a circle are probably even older. In Babylonia the number base of 60 was useful for representing fractions because 60 is divisible by 1 through 6. For example, 1/12 is able to be written as 0.5 since 5/60 equals 1/12. Could it be that 360 was used to get even more nice fractional parts of the circle in whole degrees. I will leave the answer to that for the more learned in the subject of history of mathematics. Morris Kline's books would be a good place to start.

tee


Well, if your question is why it is called "pi", all I can say is the number was known long before it was called that. According to "Mathematical Thought from Ancient to Modern Times." The symbol pi was first used by William Jones in 1706, but it does not explain why.

The reason the number 3.14159 . . . is interesting is because it crops up in just about every area of mathematics. It was first recognized as the irrational ratio of the circumference of a circle to its diameter. Pi also appears in all sorts of formulas involving series of numbers, for example the sum of 1/1 + 1/4 + 1/9 + . . . + 1/n^2 + or other similar sums of even inverse powers.

asmith



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