Recall, π is defined as the ratio of the circumference(say c) of a circle to its diameter(say d). That is, π=dc. This seems to contradict the fact that π is irrational. How will you resolve this contradiction?

Question

Recall, π is defined as the ratio of the circumference(say c) of a circle to its diameter(say d). That is, π=dc​. This seems to contradict the fact that π is irrational. How will you resolve this contradiction?

Filo · Accepted Answer

Here, π=722​ Now, it is in the form of qp​, which is a rational number, but this is an approximate value of π.If you divide 22 by 7, the quotient (3.14⋯) is a non-terminating number i.e. it is irrational.Approximate fractions include (in order of increasing accuracy)722​,106333​,113355​,⋯If we divide anyone of these we get, the quotient (3.14⋯) is a non-terminating number. i.e. it is irrational.So,There is no contradiction as either c or d irrational and hence π is a irrational number.

Question Text	Recall, $π$ is defined as the ratio of the circumference(say c) of a circle to its diameter(say d). That is, $π = \frac{c}{d}$ . This seems to contradict the fact that $π$ is irrational. How will you resolve this contradiction?
Answer Type	Text solution:1
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Recall, $π$ is defined as the ratio of the circumference(say c) of a circle to its diameter(say d). That is, $π = \frac{c}{d}$ . This seems to contradict the fact that $π$ is irrational. How will you resolve this contradiction?

Text solutionVerified

Practice questions from similar books

Recall, π is defined as the ratio of the circumference(say c) of a circle to its diameter(say d). That is, π=dc​. This seems to contradict the fact that π is irrational. How will you resolve this contradiction?

Text solutionVerified

Practice questions from similar books

Recall, $π$ is defined as the ratio of the circumference(say c) of a circle to its diameter(say d). That is, $π = \frac{c}{d}$ . This seems to contradict the fact that $π$ is irrational. How will you resolve this contradiction?