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It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it has lent to computations put our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of the achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.
In H. Eves Return to Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1988.
Loci: Convergence
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A Disquisition on the Square Root of Three
About the Author / References
About the Author
Robert "Bob" Wisner is Professor Emeritus of Mathematics at New Mexico State University. He was founding editor of SIAM Review, a publication of the Society for Industrial and Applied Mathematics. He was the first full-time Executive Director of the MAA's Committee on the Undergraduate Program in Mathematics (CUPM), 1960-1963. Bob also authored or coauthored numerous K-12 textbooks for Scott, Foresman; was Consulting Editor in Mathematics for Brooks/Cole for over 25 years; coauthored a liberal arts mathematics textbook; and recently coauthored a series of interactive calculus, business calculus, pre-calculus, and AP calculus textbooks, available on CDs from Hardy Calculus.
References
1. Archimedes, The Works of Archimedes, Edited by T. L. Heath, Dover Publications, Mineola, New York, 2002, pp. lxxx - lxxxi, also pp. 94 and 96; originally published in 1897 by Cambridge University Press, second edition including The Method originally published in 1912.
2. Leonard Eugene Dickson, History of the Theory of Numbers, vol. II: Diophantine Analysis, Dover Publications, Mineola, New York, 2005, p. 342; originally published in 1919-1923 by Chelsea Publishing, New York.
3. E. J. Dijksterhuis, Archimedes, Princeton University Press, 1987, pp. 234-236; originally published in 1938.
4. Thomas L. Heath, Diophantus Of Alexandria: A Study in the History of Greek Algebra, Cambridge University Press, 1910, p. 278; originally published in 1885.
5. Sherman Stein, Archimedes: What Did He Do Besides Cry Eureka?, Mathematical Association of America, Washington, D.C., 1999.
6. Robert J. Wisner, “The Classic Greek Ladder and Newton's Method,” Loci: Convergence (August 2009), DOI: 10.4169/loci003330, http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=3330
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Wisner, Robert J., "A Disquisition on the Square Root of Three," Loci (June 2010), DOI: 10.4169/loci003514