Main Page | See live article | Alphabetical index The following argument that 22/7 > π will be readily understood by persons with no knowledge of mathematics beyond first-year calculus. Some non-mathematicians have suggested that it is "well-known" that π = 3.14159..., and therefore it must be less than 22/7 = 3.142857... . But in order to know that π = 3.14159..., as opposed to believing it because all the textbooks say so, we would need to go through a process of computation much more complicated than the argument below. Table of contents 1 The idea 2 The details 3 Appearance in the Putnam Competition 4 See also The idea The details (recall that arctan(1) = π/4) Now we see the difference between 22/7 and π is greater than zero, so 22/7 > π. Appearance in the Putnam Competition The evaluation of this integral was once one of the problems set in the 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. See also &pi, table of integrals. This article is from Wikipedia. All text is available under the terms of the GNU Free Documentation License.