Example 3. Recall, it is defined as the ratio of
the circumference (say c) of a circle to its diameter
(say d). That is, =
. This seems to contradict the
fact that he is irrational. How will you resolve this
contradictions?
Pls answer it !!!
And also Try Elaborating The Answer
Answers
First of all, like a commenter pointed out, Pi being a ratio of two numbers does not mean it is rational. Pi has been established as irrational, and we know
Pi = C/d, where C is the circumference and d is the diameter of some circle.
It follows that either C or d or both have to be irrational!
This is kind of amazing to think about, but it's true: for any circle, either the circumference, or the diameter, or both are irrational (in the abstract world of mathematics...).
BUT (and herein lies the crux of the apparent contradiction)... in the real world where we have to use measurements, of course your measurements will always be rational numbers. ANY measurement you make is just an approximation anyway, and is rational, such as 14.52 cm or 8 1/16 in.
And, if you try to find the value of Pi using measurements from real world, all you get is a rational approximation to the value of Pi