Recall, \pi is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). This seems to contradict the fact that \pi is irrational. How you resolve this contradiction?
Answers
Answer:
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 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 p/q ( 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 .
Step-by-step explanation:
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