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Pythagoras: It’s not just a theory
By RickMeasham | December 23, 2010
Pythagoras said (amongst other things one would imagine) that the length of the hypotenuese of a right angled triangle was the square root of the sum of the squares of the other two sides.
h = √( a² + b² ) or you might know it as a² + b² = c²
I was a bright math student. To brag, in year nine I was one of 18 students in the Geelong region selected to participate in Deakin University’s advanced student program. But I was a pain in the arse to my teachers. I’m sure the phrase “could do better if only he applied himself” was coined specially for me.
One particularly annoying thing I did was insist on knowing how something worked. Or why it worked. I disagreed with teachers when they were wrong (Galileo didn’t prove that a feather and a rock dropped from the third-floor science wing would hit the ground at the same time. If he did, skydivers are all screwed)
Pythagoras Theorum was one of those things I needed to understand. Remembering the formula was a cinch, but I wanted more. And I got more. Here’s what a teacher said when I asked:
It’s called Pythagoras Theory because it’s only a theory. Every triangle that it’s ever been tested on works, so there’s no reason to doubt that it will continue to work on every triangle we ever find. But until there’s a way to prove it, it will always be called a theory. If it’s ever proven, it will be called Pythagoras Rule. (OK that was 20+ years ago, so it’s just a paraphrase)
About five years ago I was reading the book Fermat’s Last Theorum when I discovered to my astonishment that the Pythagorean Theorum had been proven in many many ways for hundreds of years. Just because it was called a “Theorum” didn’t mean it couldn’t be proven.
I went to a number of high-schools, so unless you were in that back row of math-nerds with me, you won’t know where it was. But that doesn’t matter. You can’t change the past, only the future.
Today I discovered the Khan Academy (via Reddit) and now I want you to discover it too. Especially if you’re a teacher who has students that want to know more than you have time to give them. Or who want anwers to questions you’re not really qualified to give.
Here’s just one way to Capital-P-Prove Pythagoras Thorum:
If you’re a teacher, get the Kahn Academy site on your school’s whitelist. Then follow my simple plan for teaching regular, slow, and advanced students:
Regular: Here’s the theorum, learn it so you can write the formula from knowing the theorum.
Slow: Here’s the formula, remember it and learn where the [√] and [²] buttons are on your calculator. Write it on you scrap paper before you even look at the test so you don’t need to try to remember it after you’ve started.
Advanced: Here’s the theorum, and here’s a video that proves it works for all right angled triangles.
If you’re a parent and your kids are asking for help (or need help they’re not asking for) then send them to the 1600+ videos that Salman Khan has put together on an amazing range of subjects.
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