Forum Outposts

The Geometry Forum Newsletter

Winter 1995, page 4

Teachers, Students, Families -- Getting Hooked on Math

Ruth Carver, a high school math teacher at Mt. St. Joseph's in Flourtown, Pennsylvania writes: "My students had a lot of fun constructing this problem (below) on Sketchpad and learned a lot about constructions while doing it. By the way, we had parents' night this past Tuesday and many parents remarked on how they are getting hooked on the Problem of the Week, and look forward to it each week. Isn't that great? -- whole families talkin' math."

Geometry Forum Problem of the Week, 11/21-25: Bao-Ngoc and Bi-Ping were playing around with shapes, seeing whether they could make tiles that would fit together and fill a plane without any gaps. Bi-Ping found an interesting figure, which she described to Bao-Ngoc: "ABC is an equilateral triangle. Make a square on each side of it. Make segments that join the outside vertices of adjacent squares to form a hexagon."

"I think that's a nice figure. It looks sort of like a gemstone. Can we tile the plane with it?" Bi-Ping asked. "Maybe. Is it a regular hexagon?" replied Bao-Ngoc. "I don't know," answered Bi-Ping. "The book asks some questions like that:

Is the hexagon equilateral?
Is the hexagon equiangular? and
Can we find the area of the hexagon if the sides of the triangle are each one unit in length?"

"Well, maybe that will tell us. Let's answer those three questions, see what we get, and then see what happens when we try to tile the plane with this figure," said Bao-Ngoc.

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Sarah Seastone
30 December 1994