How to prove Pytharoras'Theorem

A short video showing how I think Pythagoras proved the theorem that bears his name.

Category:

Howto & Style

Tags:

• high
• school
• maths
• Pythagoras
• theorem

[deadlybug]

Sorry, but your initial proof didn't proove a damn thing, you just replaced the the "L" sketch with two non-proven-to-be squares, and who claims for them to be the same squares as in the original example?

Didn't follow you on the second try, but here's an easy proof: imagine the blue triangle and the C square both inscribed in one large square. It's border is a+b, so the surface area is (a+b)², equal to the four triangles plus C, meaning 4·½ab+c², will lead you to a²+b²=c².

[ukbraintrainer]

No. You're wrong. The proof is perfectly robust. You may need to follow it a couple of times before you get it.

[randomgasattack]

Did you appropriate this demonstration from Jacob Bronowski's 'Music of the Spheres' episode from his Ascent Of Man?

[ukbraintrainer]

I was very strongly influenced by the entire TV series. The geometrical part of the proof is very much influenced. The algebraic part (from 3.40 onward) is unique as far as I know, but is based on the geometrical proof.

[malgrif091]

for everyday people they can get by with just knowing the formula and plug in numbers. for university/college students who study math/physics it's good to understand every formula you're using so you can perhaps figure out a solution to problems that aren't so straight forward. It also helps develop critical thinking skills.

[AlbertaSun]

I think you're right Michael; Pythagoras' method is as you illustrated. Messy calculations usually tells me I'm doing something wrong.

[y11YUNTAEHYEONG]

Why is the title pytharoras?

[HallmarkJD]

@feedtherich isn't it just a-b because the side of the larger triangles have sides a and b by supposition. So for one side of the pink square, just subtract the short side of the grey triangle from the long side of the green triangle.

[airsoftcandyboy]

sounds like young george harrison and john. They are two of the four Beatles, as if you didn't know.

[atam93]

squäääää

[feedtherich]

Uh, but how did he get the area of the pink square? I mean we know it's true, but how do we know it's true? That's what the proof is supposed to provide.

[MathDoobler]

@ukbraintrainer

Yeah the initial proof is robust, but you don't explain WHY you can cover the L-shaped region with the two brown squares of area a^2 and b^2. But that's easy enough to remedy when you show that the small purple square has a side length of (b-a) and then use that to show the L-shaped region can be divided into two squares of area a^2 and b^2. I can sympathize with deadlybug because this wasn't explicitly shown but the proof CAN be made to work.

[razorbladekissss]

or if youre a dumbass like me...zippo lighters and party hats!

[2Raphaelrs55]

First time I see Mathematics in English! Very nice! (I'm Brazillian)

I love Pythagoras' Theorem!

I've made a presentation about it, maybe I'll upload a video soon...

[zechfix]

Thumbs up! This is the first complete proof i've seen that is ultra trivial! great stuff!