Question

3. Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, π = This seems to contradict the fact that π is irrational. How will you resolve this contradiction?
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Answer 1

Answer:

Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, π=cd. This seems to contradict the fact that π is irrational. ... Here the circumference of the circle (c) of the circle is given by 2πr, where r is the radius of the circle.

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Answer 2

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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 22/7

Also diameter(longest chord of circle) of the circle is equal to 2r.

Hence, 

c = (2πr), d = 2r

⇒ c/d = π

This is analogous to the approximated value of 22/7 which though looks like a rational number of the form qp (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 = c/d

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