Electronic Proceedings of the Tenth Annual International Conference on Technology in Collegiate MathematicsChicago, Illinois, November 69, 1997Paper 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
USA
Phone: (512) 2452551
Fax: (512) 2453425
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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 sevenstep 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