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Cube Slices, Pictorial Triangles, and Probability

by Gulbank D. Chakerian and David E. Logothetti

Award: Carl B. Allendoerfer

Year of Award: 1992

Publication Information: Mathematics Magazine, Vol. 64(1991), pp. 219-241

Summary: A description of binomial coefficients and other sets of numbers obtained by slicing k-dimensional cubes with hyperplanes.

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About the Authors: (from Mathematics Magazine, Vol. 64 (1991)) Don Chakerian received his Ph.D. in 1960 from the University of California at Berkeley under the direction of Istvan Fary (one of whose results plays a role near the end of this article). After three years as an instructor at CalTech he traveled to the University of California at Davis from which he has since retired. This article results from the longstanding fascination of the two authors with problems fusing geometry and combinatorics.

Dave Logothetti received his Ph.D. in 1972 from the University of California at Los Angeles in curriculum and instruction with mathematics as a cognate field, supervised by Louise Tyler, along with Barrett O'Neill and Richard Arens, among others. With Don Chakerian, a mentor, he shared enthusiam for corny jokes, cartoons, and especially geometry. He was also a disciple of George Polya, whose influence may be discerned in his three books on teaching mathematics and problem solving in junior and senior high school (one co-authored with his son, Ted), and articles published by the California Mathematics Council, the National Council of Teachers of Mathematics, and of course the MAA. Dave Logothetti passed away on July 20, 1991.

Subject classification(s): Discrete Mathematics | Combinatorics | Geometry and Topology | Solid Geometry
Publication Date: 
Friday, February 2, 2007