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Transcript for Pythagorean Theorem Demonstration

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.