Perimeter Magic Polygons: 10-Integer Pentagon

by kdurden
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Terry Trotter (1941 – 2004) was a math teacher. In 1972, he published his ideas about a type of math puzzle he called "Perimeter Magic Polygons." These are--

a regular polygon with
a set of consecutive positive integers
to be placed around the perimeter of the figure
so the sums of the integers on each side are equivalent.

There are only six known solutions (with reflections and rotations) for the sums 14, 16, 17, and 19. There are no solutions discovered for sums less than 14 or greater than 19, nor are there known solutions for the sums 15 or 18.

Terry taught several years in the U.S. before moving to El Salvador (1981) to work at the Escuela Americana in San Salvador. His main focus and experience was in the upper elementary and middle school levels. “Trotter Math” were topics and ideas that interested Terry in particular, and proved to be interesting to students that appreciated and responded to his style of lessons and activities.

Notes and Credits

Concept: Idea based on original math puzzles created by Terry Trotter (1941-2004), 1972.

Solutions based on analysis by Harvey Heinz shared at

Artwork: The Penrose triangle was first created by the Swedish artist Oscar Reutersvärd in 1934; psychiatrist Lionel Penrose and his mathematician son Roger Penrose independently devised and popularized it in the 1950s, describing it as "impossibility in its purest form."

Font: Macula, the Impossible Typeface, by Netherlands designer Jacques Le Bailly, a.k.a. Baron von Fonthausen.

Music "Hawaii 5 O," by Morton Stevens, Brian Tyler, Keith Power, 1968, "Pentagon," from Call of Duty: Black Ops by Sean Murray, 2010.

Shared: 11 Apr 2017 Modified: 11 Apr 2017
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