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72,044 Views • Apr 15, 2024 • Click to toggle off description
If you like this video, consider subscribing to the channel or consider buying me a coffee: www.buymeacoffee.com/VisualProofs. Thanks!
For a longer version of this video with a bonus dissection proof based on this proof, see
• Pythagorean Theorem XII (visual proof)
You can also see other Pythagorean theorem proofs here:
• Ten Epic Pythagorean Proofs Without W... (compilation)
• Pythagorean Theorem XI (Dudeney's dis...
• Pythagorean Theorem I (visual proof)
• Pythagorean Theorem II (visual proof)
• Pythagorean Theorem III (visual proof)
• Pythagorean Theorem IV (visual proof;...
• Pythagorean Theorem V (visual proof; ...
• Pythagorean Theorem VI (visual proof;...
• Pythagorean Theorem VII (visual proof)
• Pythagorean Theorem VIII (Bhāskara's ...
• Pythagorean Theorem X (visual proof w...
or check out my Pythagorean theorem playlist:
• Pythagorean Theorem
This animation is based on a proof due to Euclid. For a static version of this proof, see Roger Nelsen's first "Proof Without Words: Exercises in Visual Thinking" compendium (page 5) : bookstore.ams.org/clrm-1. You can also check out Howard Eves' "Great Moments in Mathematics (Before 1650)" page 31-33.
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#math #pythagoreantheorem #pythagorean #triangle #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #mathshorts #mathvideo
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Views : 72,044
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Uploaded At Apr 15, 2024 ^^
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RYD date created : 2024-11-17T13:10:48.856578Z
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72 Comments
Top Comments of this video!! :3
Isn't it more beautiful to draw 3 more triangles that are congruent to ABC ∆ around the c² square?
127 |
Gotta love the classics
30 |
This is also why the Pythagorean Theorem isn't true in non-Euclidean Geometries, because in those sheers and rotations are not area preserving.
16 |
I kinda prefer the the regular proofs, they just feel more certain in my mind. You know c^2=(a+b)^2-2ab
2 |
Aw I love this channel
8 |
I like your animation. I have a similar proof, using Geogebra for the two shifts and one rotation. Cavalieri Principle is involved in the shifts.
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The Pythagorean Theorem is not restricted only to squares. It'll work for circled or any other polygon.
7 |
As a math student & aficionado I love visual proofs. As a math teacher I’m not as big a fan because visual proofs are not as precise or rigorous. We may not see tiny errors in a visual proof, but a logical, algebraic proof deals with fundamentally exact relationships. For example, there are great approximations for the length of an ellipse, but it can’t be given exactly. This means visual “proof” can mislead us into accepting an approximation as an equivalence. Therefore, visual proofs need to be cross-checked with more rigorous methods.
2 |
I think this is more of an illustration than a proof as such
8 |
Very Cool ❤❤❤
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I prefer the shear up, translate, shear down proof. It's much easier to visualize and there's no overlap.
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太讚了❤簡潔易懂
3 |
Here’s another one:
So, you can take 4 of the same triangle and arrange them so the outer edges form a square. This is 2ab. The middle part (negative space) is c^2. So, 2ab+c^2=(a+b)^2. So, c^2=(a+b)^2-2ab=a^2+2ab+b^2-2ab=a^2+b^2, hence a^2+b^2=c^2.
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Beautiful
2 |
Yooo that's lovely!
3 |
Amazing! Can this technique be used to prove the law of cosines, that
c^2 = a^2 + b^2 -2ab*cos(γ)?
I guess the rotation is where the cosine might come from!
1 |
That's a nice one!
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Wait this is literally just Euclid's first theorem, which I'm studying in school now.
In case people didn't know, Euclid's first theorem states that the area of the square of a leg is equal to the area of a rectangle with 1 side being the hypotenuse and the other side being the projection of that same side on the hypotenuse
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... Beautiful :D
5 |
@narfharder
7 months ago
Proof by shear force of will
An unexpected turn of events
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