Connecting Greek Ladders and Continued Fractions - References

References

[1] Brezinski, Claude, History of Continued Fractions and Pade Approximants, Springer-Verlag, New York, 1980

[2] Burton, David, Elementary Number Theory (7th ed.), McGraw-Hill, New York, 2011

[3] Giberson, S. and Osler, T. J., Extending Theon’s ladder to any square root, The College Mathematics Journal 35 (2004), 222-226

[4] Katz, Victor, A History of Mathematics: An Introduction (3rd ed.), Addison-Wesley, Boston, 2009

[5] Olds, C.D., Continued Fractions, Random House: New York, 1963

[6] Osler, T. J., Wright, M. and Orchard, M., Theon’s ladder for any root, International Journal of Mathematical Education in Science and Technology 36 (2005), 389–398

[7] Osler, T. J., Using Theon’s ladder to find roots of quadratic equations, Mathematics and Computer Education 42 (2008), 23–27

[8] Rosen, Kenneth, Elementary Number Theory and Its Applications (4th ed.), Addison-Wesley, Boston, 2000

[9] Wisner, R. J., The classic Greek ladder and Newton’s method, Loci: Convergence (2009), DOI: 10.4169/loci003330

[10] Wisner, R. J., A disquisition on the square root of three, Loci: Convergence (2010), DOI: 10.4169/loci003514

[11] Huffman, Carl, Pythagoras, The Stanford Encyclopedia of Philosophy (Fall 2011 Edition), Edward N. Zalta (ed.),
URL = http://plato.stanford.edu/archives/fall2011/entries/pythagoras/
Accessed Jan. 2014 via http://plato.stanford.edu/entries/pythagoras/

[12] Huffman, Carl, Pythagoreanism, The Stanford Encyclopedia of Philosophy (Summer 2010 Edition), Edward N. Zalta (ed.),
URL = http://plato.stanford.edu/archives/sum2010/entries/pythagoreanism/
Accessed Jan. 2014 via http://plato.stanford.edu/entries/pythagoreanism

Acknowledgment

The authors extend sincere thanks to David Pengelley for his valuable comments and advice concerning this paper.

About the Authors

Kurt Herzinger is a member of the Department of Mathematical Sciences at the United States Air Force Academy in Colorado Springs, Colorado.  He earned his Ph.D. in mathematics from the University of Nebraska-Lincoln in 1996. His research program primarily focuses on problems in numerical semigroups motivated by topics in commutative algebra. Recently, Kurt has taken an interest in problems involving Greek ladders thanks to meeting Prof. Robert Wisner at a MAA regional meeting in 2009.

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 CD from Hardy Calculus.