360 degrees in a circle and origin of pis
Name: gordon t davis joseph f and strountree
Date: Around 1995
Why is a circle divided into 360 degrees?
From where did the name pi come?
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.
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.
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Update: June 2012