Electronic Proceedings of the Tenth Annual International Conference on Technology in Collegiate Mathematics

Chicago, Illinois, November 6-9, 1997

Paper P006

Calculator/Geometry Strategies for Understanding Properties of x^(m/n)

John J. Edgell

Mathematics Department
Southwest Texas State University
601 University Drive
San Marcos, TX 78666
Phone: (512) 245-2551
Fax: (512) 245-3425

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Some students may benefit in the understanding and applying real numbers of the form x^(m/n) from a combination of calculator and theoretical geometric techniques. The poster/paper will demonstrate a seven-step calculator routine for expressing x^(m/n) and a spiral sequence of similar right trigons for conceptualizing x^(m/n). Further calculator routines and trigonal spirals will demonstrate properties relating x^(m/n) and x^(M/N). Analysis of such trigonal spirals will reveal strategies for exploring comparisons of x^(m/n) and x^(M/N). Finally, a summary analysis for the theoretical foundations of each spiral will be included.

Keyword(s): geometry, college algebra, calculators