King's and Knight's Polygons

A polygon is a shape that consists only of straight edges and the shape must be closed.  In addition, the edges must not cross over each other. A polygon with the fewest sides is the triangle although some of the children tried to draw a polygon with only two edges. The fact that they were determined to do this was amazing.

We counted polygons by number of sides (3-12): triangle, quadrilateral, pentagon, hexagon, heptagon, octagon, nonagon, decagon, undecagon, and dodecagon.

KING'S POLYGONS -- The Thursday K class were then challenged to create polygons on 8x8 grids using only King's moves. They must make straight sides from each grid point to an adjacent point. The challenge is to create polygons with the most sides. The fewest sides will be a triangle at three. The maximum number of sides on this grid is 64. It is not easy to reach this maximum. I then gave the children grids of 9x9, 10x10, 11x11, and 12x12. The maximums for these grids are 79, 98, 119, and 142, respectively. They should try to create polygons with the most sides on each grid and count the number of sides they create.

KNIGHT'S POLYGONS -- All other Wednesday, Thursday and Friday classes were challenged to create polygons on 8x8 grids using only Knight's moves. They must make straight sides from each grid point to a point an L shape away. The challenge is to create polygons with the most sides. The fewest sides will be a square or rhombus at four. The maximum number of sides on this grid is 26. It is not easy to reach this maximum. I then gave the children grids of 9x9, 10x10, 11x11, and 12x12. The maximums for these grids are 36, 48, 56, and 74, respectively. They should try to create polygons with the most sides on each grid and count the number of sides they create. 

I told them if they find polygons with more sides then my maximum on a given grid, I will put their face on a Mathlete Dollar. I suspect that many will try.