Question

recall pi , is defined as the ratio of the circumfrence (say c) of a circle to its diameter say(d) . that is pi = c/d . this seems to contradict the fact that pi is irrational number , how will u solve this contradiction ?

Answer 1

Answer:

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Step-by-step explanation:

There is no contradiction:-

When we measure a length with scale or any other instrument, we only obtain an approximate rational value. We never obtain an exact value.

For this reason, we cannot say that either c or d is irrational.

Therefore, the fraction c/d is irrational. Hence, the value of pie is approximately equal to 22/7= 3.142857....

Therefore,pie is irrational.

Answer 2

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 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.