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Prized Geometric Logic

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Author:Ivars Peterson (MathTrek)
Description: Computer programs can handle all sorts of data [such as] a set of discrete elements, such as temperatures. Some elements of a set may be larger in value than others, or they may exhibit some other relationship that allows you to rank them or put them in order. In mathematics, such a collection of elements is known as a partially ordered set, or poset. One example of a poset consists of an integer and all its positive divisors (excluding 1). For instance, the positive divisors of 42 are 2, 3, 6, 7, 14, and 21. The relationships among the integers in the poset {2, 3, 6, 7, 14, 21, 42} can be expressed symbolically in a special type of diagram known as a Hasse diagram, named for mathematician Helmut Hasse (1898-1979). Research involving a link between posets and geometric figures was the focus of an award-winning project in the 2001 Intel Science Talent Search. Gabriel D. Carroll, a student at Oakland Technical High School in Oakland, Calif., titled his project "Homology of Narrow Posets."

Levels: High School (9-12), College
Languages: English
Resource Types: Articles
Math Topics: Sequences and Sets, Algebraic Topology

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