Terry Trotter's
Perimeter Magic Polygons
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--
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.
- 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.
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.
http://www.trottermath.net/simpleops/pmp.html
Perimeter Magic Polygons:
10-Integer Pentagons
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.
https://scratch.mit.edu/projects/155109299/
12-Integer Squares
There are 140 known solutions (with reflections and rotations) for the sums between 22 and 30. There are no known solutions discovered for sums less than 22 or greater than 30.
https://scratch.mit.edu/projects/155101624/
8-Integer Squares
There are six known solutions (with reflections and rotations) for the sums 12 (one, 13 (two), 14 (two, and 15 (one). There are no solutions discovered for sums less than 12 or greater than 15 using consecutive integers.
https://scratch.mit.edu/projects/154864910/
6-Integer Triangles
There are twelve known solutions (with reflections and rotations) for the sums 9, 10, 11, and 12. There are no solutions discovered for sums less than 9 or greater than 12.
https://scratch.mit.edu/projects/154861547/
Perimeter Magic Polygons: 9-Integer Triangles
There are eighteen known solutions (with reflections and rotations) for the sums 17 (two), 19 (four), 20 (six), 21 (four), and 23 (two). There are no solutions discovered for the sums 18 and 22 or for less than 17 or greater than 23.