Posts Tagged ‘penrose’

Toilet Paper Math

May 8, 2008

Really, is there a more appropriate follow-up to yesterday’s featured theorem?

Last night young Quentin, age 4½, went to get some toilet paper to clean toothpaste out of the sink after brushing his teeth (because — get this — he likes to clean up after himself. I can hardly believe it.). As he pulled off a strip of TP, he suddenly held it against himself and got all excited: “This is as big as my belly!” I pointed out that his belly was three squares big, and asked how long his arm was. He measured, and exclaimed, “My arm is three squares long!” When he tried to measure his leg, it fell short so I suggested he might need one more square. He immediately went to the roll, counted off a strip four squares long, and held it against his leg. Yup, four squares worked.

The sink stayed dirty for a while after that while he went around measuring his hand (one square), our arms, etc. The nice thing about toilet paper is that he could take strips of various sizes and just pick the one that seemed best. His measurements weren’t exact (I’m not going to hire him to build a bookcase, for example) but he did seem to have the basic idea of measurement and that’s a topic that several K-6 teachers I’ve talked to say is the one that students need the most help with after number sense. (Speaking of which, Denise on Let’s Play Math had a great post Tuesday about helping kids learn number sense.) And I think non-standard measurement is one of the NYS math standards. [Quick check -- yup, it's 1.M.2, 1.M.11, 2.M.1, 2.M.10, and 3.M.10. I spent a while last year putting all the NYS math standards into Excel worksheets for easy searching and posted them here if anyone would find that useful.]

Thinking about blogging this, I googled “Toilet Paper Math” and found some other interesting ways to use toilet paper to do math. You can determine the least expensive choice of TP at the grocery store. You can fold it in half twelve times. You can find the thickness of a sheet of TP (although it seems like density — aka fluffiness — might make that inexact). You can calculate how much text you can print on a roll of toilet paper.

And finally, you can read about how Sir Roger Penrose sued the Kimberly Clark Corporation back in 1997 because one of the designs that was printed on Kleenex quilted toilet paper looked like Penrose tiles (see Wolfram’s Mathworld or this more detailed summary from Professor Richard H. Stern’s Computer Law Class at George Washington University.)

Update 5/10: I think these are the kinds of pictures that mbork was referring to below. In the first two examples the triangle has a right angle, but in the third the angle a bit larger.


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