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.
@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.
This is much better than the scarecrow on the Wizard of Oz who got it wrong on two fronts. I challenge my seventh graders to find the mistakes in the Wizard of Oz version.
The explanation around 2:40 is completely lacking in any detail. You may as well have just started with a^2 +b^2=c^2 for all help that this proof offers.
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.
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.
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.
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.
I think you're right Michael; Pythagoras' method is as you illustrated. Messy calculations usually tells me I'm doing something wrong.
AlbertaSun 2 months ago
Why is the title pytharoras?
y11YUNTAEHYEONG 6 months ago
sounds like young george harrison and john. They are two of the four Beatles, as if you didn't know.
airsoftcandyboy 7 months ago
squäääää
atam93 8 months ago
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.
feedtherich 1 year ago
@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.
HallmarkJD 6 months ago
or if youre a dumbass like me...zippo lighters and party hats!
razorbladekissss 1 year ago
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...
2Raphaelrs55 1 year ago
Thumbs up! This is the first complete proof i've seen that is ultra trivial! great stuff!
zechfix 1 year ago
This is much better than the scarecrow on the Wizard of Oz who got it wrong on two fronts. I challenge my seventh graders to find the mistakes in the Wizard of Oz version.
piperjyfso 1 year ago
Comment removed
bestharryintoronto 2 years ago
Sorry to be so harsh! What's missing to make it clearer is to point out that in the LH diagram:
Top side of the pink square + top side of triangle 3 = bottom side of triangle 2 = length A
This edge is still in the RH diagram.
And similarly,
Top side of triangle 4 - bottom side of the pink square = bottom side of triangle 1 = length B
This edge is also in the RH diagram.
If you have met this before is all really obvious but some ppl need a bit more help.
chrisofnottingham 2 years ago
The explanation around 2:40 is completely lacking in any detail. You may as well have just started with a^2 +b^2=c^2 for all help that this proof offers.
chrisofnottingham 2 years ago
You need to follow things a little more closely to see the detail. The proof is perfectly robust.
The rearranged square has an area of C^2. The two brown squares have an area of A^2 + B^2. Hence the theorem is proven.
ukeducoach 2 years ago
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.
deadlybug 3 years ago
No. You're wrong. The proof is perfectly robust. You may need to follow it a couple of times before you get it.
ukbraintrainer 3 years ago 4
It's robust...but badly described though...
coder2k 2 years ago
@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.
MathDoobler 1 year ago
Did you appropriate this demonstration from Jacob Bronowski's 'Music of the Spheres' episode from his Ascent Of Man?
randomgasattack 3 years ago 2
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.
ukbraintrainer 3 years ago
wtf
metalhealth666666 3 years ago
3 Cheers for the modern Pythagoras michael
warior949 3 years ago
thanks alot michael u helped me alot this will help alot in my assaingments
warior949 3 years ago
thanks. i need this for school.
Bart4life10 3 years ago
Just wondering, what is the use of this information?
.
What does knowing this do to enrich life for the individual everyday?
Cheers.
from,
del-boy.
MarioOhlert 3 years ago
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.
malgrif091 3 years ago 6
Exactly
Pathagarus 3 years ago
im using this for my geometry assignment =]
jonyb0b13 4 years ago
im using this for my geometry assignment =]
jonyb0b13 4 years ago