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Pythagorean triples and baby-fat

linesI was particularly delighted when my daughter pulled me aside from my busy grown up stuff yesterday, not to ask for my help, but rather to demonstrate her latest discoveries in mathematics. Not that I get all warm and fuzzy about math, mind you – I was never particularly good at it. But somehow my kid has bypassed her father’s lack of luster for numbers and is actually kind of good at it. Go figure (pun somewhat intended).

Usually when the math books come out, it’s about equations, and I get lost pretty fast. This time, there were no books at all, rather just a ruler, some blank sheets of paper, and a compass (the kind you make circles with – that’s important, because she and her fellow middle-schoolers have also been working on map triangulation with the ones that show you north). The purpose of this collection, she told me, was to use Pythagorean triples to create triangles with perfect right angles.

Now, I’m definitely not the right candidate to get into the mathematical gobbledygook of this, but the basic concept is really pretty simple: Pythagorean triples are sets of three numbers which meet this formula: a2+b2=c2. Three, four, and five are the smallest of these (small is easy, easy is good).

creating a right triangleNow sit down with a kid, a friend, or the neighborhood cat, and try out what my daughter showed me. She drew a line on a page, marked a point on the line (we’ll call that point 1), set her compass at five centimeters (way better than inches on smaller pages, but she considers fat pink English rulers better for drawing lines, of course), and marked a second point from the first point (we’ll call that one point 2). “That,” she said, “is the hypotenuse. That’s the longest line of the triangle.” She then set her compass at four centimeters, placed the tip at point 2, and drew a circle. After that, she set her compass at three centimeters, placed the tip back at point 1, and drew another circle. “That’s how I find out where the third point goes.” She marked a point where the two circles intersected, and then drew a line from the first point to the third and the second point to the third, respectively. VoilĂ ! A right triangle!

But I actually didn’t start writing this to explain elements of planar geometry. I started writing it because I was so taken (as always, really) by the bonding experience of sharing learning with a child, especially my own. The care she took to show me what she had learned, to make sure that I really understood it. The way she drew her lines so confidently and meticulously. And how, I realized, those little baby-fat dimples around her knuckles were finally, and suddenly, gone! That was warm and fuzzy, after all…

If you want to learn more about creating right triangles with Pythagorean triples, goes into much more detail here!