IJPAM: Volume 81, No. 6 (2012)

CALCULATING $\sqrt{2}$

Yutaka Nishiyama
Department of Business Information
Faculty of Information Management
Osaka University of Economics
2, Osumi Higashiyodogawa Osaka, 533-8533, JAPAN

Abstract. This article concerns root 2. The ratio of height and width of copy paper is root 2, and can be calculated by using similar diagrams. Root 2 is an irrational number whose cardinality is uncountably infinite. Roots are calculated numerically by the Newton-Raphson method which uses an approximating 2nd order function and its tangent.

Received: August 18, 2012

AMS Subject Classification: 68W02, 00A09, 97A20

Key Words and Phrases: ratio of height and width of copy paper, similar diagrams, irrational number, Reductio ad absurdum, cardinality of numbers, Cantor's diagonal method, countably infinite and uncountably infinite, 2nd order function and its tangent, Newton-Raphson method

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 81
Issue: 6