Proof that 22/7 Exceeds π: Proof that 22/7 Exceeds π, Proof of Bertrand's Postulate, Projection Linear Algebra, Linear Algebra, Functional Analysis, Vector Projection, Technical Drawing - Couverture souple

Couverture souple

ISBN 10 : 6130344163 ISBN 13 : 9786130344160

Editeur : Betascript Publishing, 2010

Synopsis

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. "

Détails de l'édition

• Éditeur: Betascript Publishing
• Date d'édition: 2010
• Langue: anglais
• ISBN 10: 6130344163
• ISBN 13: 9786130344160
• Reliure: Broché
• Nombre de pages: 112
• Éditeur: Surhone Lambert M., Tennoe Mariam T., Henssonow Susan F.
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible