University of Dubuque

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Professor Dick Smith Discovers Unique Algorithm

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Posted Nov 14, 2012

While delving deeper into the task of finding skewed lattice rectangles in Modern Geometry, an algorithm grew out of the basic idea that both pairs of opposing sides of a rectangle and their diagonals are congruent and, if skewed, can be checked by using a simple algebraic equation.  Students began the process of generating integers to satisfy the equation a2 + b2=c2+d2.  A concept arose resulting in an algorithm that extend into 3 dimensions - allowing the ability to find non-congruent rectangular prisms having congruent diagonals.

Professor Smith's discovery is unique because it was the result of how a specific problem presented to college students grew into a larger exploration, with connections between algebra, geometry, and also number theory. 

This development is something that has possibly not been published before.  Dr, Wolfgang Kleimann, department chair of Iowa State University, stated, "Your algorithm describes an interesting connection in number theory.  To the best of our knowledge, this algorithm has not been published before, or cannot easily be found in the literature."