Plane trigonometry, by S.L. Loney.

8

TRIGONOMETRY.

Hence the ratio of the circumference of a circle to its
radius, and therefore also to its diameter, is a constant
quantity.
12. In the previous article we have shewn that the. Circumference
ratio Cire is the same for all circles. The value
Diameter
of this constant ratio is always denoted by the Greek
letter wr (pronounced Pi), so that wr is a number.
Circumference
Hence = the constant number 7r.
Diameter
We have therefore the following theorem; The circumference of a circle is always equal to 7r times
its diameter or 27r times its radius.
13. Unfortunately the value of 7r is not a whole
number, nor can it be expressed in the form of a vulgar
fraction, and hence not in the form of a decimal fraction,
terminating or recurring.
The number wr is an incommensurable magnitude, i.e. a
magnitude whose value cannot be exactly expressed as the
ratio of two whole numbers.
Its value, correct to 8 places of decimals, is
3-14159265....
The fraction 7 gives the value of wr correctly for the
22
first two decimal places; for 7 = 3'14285....
355
The fraction 11 is a more accurate value of wr being
355
correct to 6 places of decimals; for -=3'14159203....
113