recall , pie is defined as the ratio of the circumference (say c)of a circle to its daimeter (say d) that is pie = c upon d this seem contract the fact that pie is irrational how will you resolve this contradiction
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When we measure a length with a scale or any other device, we only get an approximate rational value.
Therefore we may not realise that c or d is irrational.
Circumference c or the perimeter of a circle is given by 2πr,
where r is the radius of the circle
π is approximated as 3.14 or
7
22
Also diameter(longest chord of circle) of the circle is equal to 2r.
Hence, c=(2πr),d=2r⇒
d
c
=π
This is analogous to the approximated value of
7
22
which though looks like a rational number of the form
q
p
(q!=0)
But when computed corresponds to a real value of ~3.14.
And real numbers consists of irrational numbers.
Hence, there is no contradiction in the equation =
d
c
.
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