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Proof that 22 over 7 exceeds π - Appearance in the Putnam Competition
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Proof that 22 over 7 exceeds π, Proof that 22 over 7 exceeds π - Appearance in the Putnam Competition, Proof that 22 over 7 exceeds π - The details, Proof that 22 over 7 exceeds π - The idea, Table of integrals, Table of mathematical symbols

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Proof that 22 over 7 exceeds π - Appearance in the Putnam Competition: Encyclopedia II - Proof that 22 over 7 exceeds π - Appearance in the Putnam Competition

The evaluation of this integral was the first problem in the 1968 Putnam Competition. If it seems trivially routine for a Putnam Competition problem, one may perhaps surmise that its inclusion was motivated by the conjunction of the punch line (summarized by the title of this article) with the fairly nice pattern in the integral itself. Many years earlier, the result was given in D. P. Dalzell, On 22/7, Journal of the London Mathematical Society 19 (1944) 133-134. ...

That the integral is positive follows from the fact that the integrand is a quotient whose numerator and denominator are both nonnegative, being sums or products of even powers of real numbers. So the integral from 0 to 1 is positive. It remains to show that the integral in fact evaluates to the desired quantity: (recall that arctan(1) = � ...

Proof that 22 over 7 exceeds π - Appearance in the Putnam Competition

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