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Proof that 22 over 7 exceeds π - The details | | Proof that 22 over 7 exceeds π - The details: Encyclopedia II - Proof that 22 over 7 exceeds π - The details | | 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) = Ï ...
See also:Proof that 22 over 7 exceeds π, Proof that 22 over 7 exceeds π - The idea, Proof that 22 over 7 exceeds π - The details, Proof that 22 over 7 exceeds π - Appearance in the Putnam Competition | | | 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 | | |
| | | Proof that 22 over 7 exceeds π: Encyclopedia II - Proof that 22 over 7 exceeds π - The details
Proof that 22 over 7 exceeds π - The details
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:
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(recall that arctan(1) = π/4) |
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Other related archives1944, 1968, Putnam Competition, Table of integrals, Table of mathematical symbols, approximation, calculus, continued fraction, integral, integrand, mathematical proof, rational number, real numbers, π
 Adapted from the Wikipedia article "The details", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
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