Page 91 - Mathematics Class - IX

PROJECT 1

AIM

Story of p .

DEFINITION
The ratio of circumference ‘c’ of a circle to diameter ‘d’ is always remains constant. This constant ratio is
known as p (pie).

VALUE OF p
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The value of p is . Different mathematicians calculated value of p in different ways. Some of them are:
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1. Archimedes : The ratio of the area of a circle to that of a square with side equal to the circle’s diameter is
close to 11 : 14.

πr 2 11 44 22
i.e. = ⇒ π= =
r 4 2 14 14 7

2r

r

This approximate value is generally used in the problems related to mensuration.
2. Liu Hui: Liu Hui used regular polygons with increasing number of sides to approximate the circle. He used

only inscribed circles while Archimedes used both inscribed and circumscribed circles. Liu’s approximation
3927
of p was = 3 1416. .
1250

INFERENCE
22
The value of p is used as or 3.141.
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APPLICATION
The value of p is used in the construction of racing tracks and making engineering equipments.

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