Question

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?

Answer 1

Circumference = π × diameter
c = πd
π = c/d
π is the ratio of the circumference of a circle to the length of the diameter.

When we measure the length with the scale Or any other device we only get an approximate rational value so we may not realise that in c & d which one is irrational.
So either c or d is irrational and hence c/d is irrational i.e π is irrational. Hence ,there is no contradiction in saying that π is irrational.

HOPE THIS WILL HELP YOU...

Answer 2

Answer:

There is no contradiction . when we measure a value with scale , we only obtain an approximate value . we obtain an extract value .

Therefore , we may not realize that either circumference or diameter is irrational . The value of π is almost equal to 22/7 or 3.142857