Bookcover of Proof that 22/7 Exceeds π
Booktitle:

Proof that 22/7 Exceeds π

Betascript Publishing (2010-09-15 )

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ISBN-13:

978-613-0-34416-0

ISBN-10:
6130344163
EAN:
9786130344160
Book language:
English
Blurb/Shorttext:
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Proofs of the famous mathematical result that the rational number 22⁄7 is greater than π date back to antiquity. What follows is a one-line modern mathematical proof that 22⁄7 > π, requiring only elementary techniques from calculus. The purpose is not primarily to convince the reader that 22⁄7 is indeed bigger than π; systematic methods of computing the value of π exist. Unlike some elementary proofs, the calculus-based proof presented here is straightforward; its elegance results from its connections to the theory of diophantine approximations. Stephen Lucas calls this proposition "One of the more beautiful results related to approximating π". Julian Havil ends a discussion of continued fraction approximations of π with the result, describing it as "impossible to resist mentioning" in that context. If one knows that π is approximately 3.14159, then it trivially follows that π < 22/7. But it takes much less work to show that π < 22/7 than to show that π is approximately 3.14159.
Publishing house:
Betascript Publishing
Website:
https://www.betascript-publishing.com/
Edited by:
Lambert M. Surhone, Mariam T. Tennoe, Susan F. Henssonow
Number of pages:
112
Published at:
2010-09-15
Stock:
Available
Category:
Mathematics
Price:
39.00 €
Keywords:
Proof that 22/7 Exceeds π, Proof of Bertrand''s Postulate, Projection Linear Algebra, Linear Algebra, functional analysis, Vector Projection, Technical Drawing

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