Comments on: Toilet Paper Math

By: Ξ

Fri, 09 May 2008 22:28:18 +0000

OK, I get it now! (When I get a chance, probably tomorrow morning, I’ll add a picture to the bottom of the post to demonstrate what I envision.) I’ve looked at your blog a few times and read what I could of it; I’ll take a look at the Math Studies stuff!

By: mbork

mbork — Fri, 09 May 2008 20:55:30 +0000

I knew it. My English is not good enough .
What I meant was something like this:
* you pick 3 stripes of lengths 3, 4 and 5
* you pick 6 points, two for each stripe – each of them somewhere on each shorter edge
* you form a triangle by joining the strips at the points selected
* you measure the angle which was supposed to be right
* the question is: what is the maximum error?
As for your idea: I quite like it, it is obviously connected with ideals in rings, but I guess it is very nice for younger kids to train their arithmetic .
And this makes me think about the following problem: given a mathematical object or theorem X, explain X in terms of TP . Most probably I will be teaching first year students “introduction to set theory”, I’ll have to think about it .

PS. Did I tell you I like your blog a lot? I’ll have to link it from my page. (Sorry, it’s mostly in Polish, but a small fraction is in English – I used to teach Math Studies SL in an IB school and I’ve put some English materials there. Feel free to use them if you find anything useful there .)

By: Ξ

Fri, 09 May 2008 11:07:56 +0000

mbork, I’m unsure what is being measured for the error: are the sides being jointed at, say, 1″ in and you’re measuring how far from a right angle the angle is, or are you keeping the right angle and measuring how far off from 5 squares the hypotenuse would be? [I suppose either way would work, but I'm wondering which you're thinking of.]

Incidentally, your comment made me think of another idea for toilet-paper math: you could pick two lengths and talk about which lengths could be made from those two lengths (so strips of size 6 and 9 could make 6, 9, 12, 15, and every multiple of 3 from then on, while strips of size 3 and 7 could make 3, 6, 7, 9, 10, 12, 13, 14, 15, and every length from then on.)

By: mbork

mbork — Fri, 09 May 2008 07:56:02 +0000

And a nice post again:)
BTW, this can lead to a non-trivial geometry problem, appropriate for olders kids: if you use 3 strips of TP, one 3, one 4 and one 5 squares long, to form a right angle, what is the maximum error, if you join any two consecutive strips at some _random_ point at their shorter sides (not necessarily vertices or midpoints)? (Hope I expressed myself clearly;).)