Question

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​

Answer 1

Answer:

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

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

.