Recall,π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d) . that is,π=c/d. this seems to contradict the fact that π is irrational. how will you resolve this contradiction?
Answers
Answer:
solution:c/d=22/7 is the approximate value of π and also it is non terminating
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
.