## Thursday, June 2, 2011

### New toys for Matty Boy! YAY!

Way back in January 2010, when I was still doing my (almost) weekly Wednesday Math posts, I wrote about Penrose tiles, the two shapes designed by physicist Roger Penrose that fill the plane in repeating patterns or non-repeating patterns, depending on how clever you want to get.

I bemoaned that there was no way to get a nice set of reasonably priced Penrose tiles to play with and mulled over the idea of having some made by a plastic fabrication shop.

Well, this is one of those times my natural laziness and broke assedness (which springs naturally from laziness, thank you very much) paid off big time. After putting this on the back burner for over a year, I searched last week and found a company that sold the thing I was looking for at a very reasonable price. SeriousPuzzles.com sells 108 Penrose tiles for \$20, and better than that, they come with magnetized backs, so you can put them on your refrigerator or, for us teachers, tack them up on the white board in your class.

My friend Mark was nice enough to hold a pair of these in his hand to give you an idea of scale. They are nice soft bendy plastic, so I would say they are safe for any child who has already learned "Just because I can hold something in my hand, it does not follow that I have to put it in my mouth."

The two shapes are called the dart (top) and kite (bottom). The sets I got came in blue, yellow and purple. They appear to be easy to clean and in my experience, rubberized magnets maintain their stickiness nearly forever. (They are magnets, so tell the kids to keep them away from the computer.)

The angle between the two long sides is 72°, so if I put five pieces together, long side to long side, I can start a tiling of the plane. Five kites make a regular ten sided shape called a decagon. Five kites make a five pointed star, but not exactly the pentagram that we see on the stars of the American flag.

If you put a kite and a dart together on the short sides, they make a rhombus. Five of these rhombi correctly placed can make a regular pentagon with a pentagram in the negative space. The pentagram is the shape of the five pointed stars on the American flag.

Next: Matty Boy has way too much fun with Penrose tiles.