The formula for the circumference of a circle is c=pi d, where d is the length of the diameter. If d is a rational number, what can you conclude about the circumference?

Kevin Charles

Kevin Charles

Answered question

2022-10-12

The formula for the circumference of a circle is c = π d, where d is the length of the diameter. If d is a rational number, what can you conclude about the circumference?

Answer & Explanation

cdtortosadn

cdtortosadn

Beginner2022-10-13Added 19 answers

π is an irrational number, multiplying by a rational number different from 0 will give as a result an irrational number. This is because if that is not the case, then there would exist rational numbers a and b, with a different from 0, such that
π a = b, then π = b a
Since the quotient of two rational numbers is a rational number, if b and a were rational, then π should also be rational, which is not the case.
We conclude that, since the diameter is positive and rational, that the circumference cant be rational, therefore it is irrational.

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