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Transcript for Pythagorean Theorem Demonstration
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| Time | Content |
|---|---|
| 00:00 → 00:03 |
Hello! Michael here |
| 00:03 → 00:05 |
This is a very short video |
| 00:05 → 00:11 |
about how I think Pythagoras discovered the proof of the theorem that bears his name |
| 00:11 → 00:16 |
First of all. Pythagoras lived about two and a half thousand years ago |
| 00:16 → 00:19 |
He wasn't the man who discovered the theorem; |
| 00:19 → 00:23 |
It had been known for about two and a half thousand years before that |
| 00:23 → 00:28 |
He was the person who discovered the mathematical proof of it |
| 00:28 → 00:31 |
If you want to know more about Pythagoras the man |
| 00:31 → 00:34 |
Wikipedia is a good place to start |
| 00:34 → 00:36 |
Well, first of all |
| 00:36 → 00:39 |
the theorem is about right angle triangles |
| 00:39 → 00:41 |
like this one. |
| 00:41 → 00:44 |
It states that the square of the hypotenuse |
| 00:44 → 00:47 |
is equal to the sum of the squares on the two other sides |
| 00:47 → 00:50 |
That means the areas of the squares |
| 00:50 → 00:54 |
So, here are the squares on the shorter side of the triangle |
| 00:54 → 00:57 |
they're easy enough to construct |
| 00:57 → 01:00 |
It will make life a little easier if we label them |
| 01:00 → 01:04 |
The standard way is a and b for the short sides |
| 01:04 → 01:07 |
and c for the hypotenuse. |
| 01:07 → 01:13 |
now this is how I think he constructed the square on the hypotenuse |
| 01:13 → 01:16 |
He knew that the two smaller angles |
| 01:16 → 01:19 |
add up to a right angle |
| 01:19 → 01:23 |
and so he knew that he could start with one triangle here |
| 01:23 → 01:29 |
and add another ... and another ... and another |
| 01:29 → 01:33 |
and finish up with this perfect square on the hypotenuse. |