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Geometric Puzzles in the Classroom

Tetrarcs and Pentarcs

by Brendan Owen

For a little background and context, see
Geometric Puzzles in the Classroom: Polyarcs.

A while ago I designed a general definition file for polyforms which consists of:

  1. grid (vertices, edges and regions) which can represent all the polyforms.
  2. all possible transforms (rotations and flips).
  3. the base units.

"Growing" the (n+1)forms is done by adding base units to the (n)forms edges, normalizing, sorting and removing duplicates.

In order to be able to use the program for the polyarcs, I represented the arcs with pairs of straight lines.

Here are some of the results of my search:

Number of polyarcs:

n n-arcs
1 2
2 7
3 22
4 93
5 364
6 1734
7 8246
8 41043
9 206602
The tetrarcs: tetrarcs

The pentarcs:

pentarcs
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Geometric Puzzles in the Classroom
Visit Henri Picciotto's Math Education Page. Send me e-mail .