All possible pythagorean triples, visualized
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Published 2017-05-26
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Regarding the brief reference to Fermat's Last Theorem, what should be emphasized is that it refers to positive integers. You can of course have things like 0^3 + 2^3 = 2^3, or (-3)^3 + 3^3 = 0^3.
Music by Vincent Rubinetti: vincerubinetti.bandcamp.com/album/the-music-of-3bl…
Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld
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All Comments (21)
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As to the "you're" typo at 1:20, I keep telling that second blue pi creature (Randolph is his name) to learn his grammar, but for whatever reason, he just never listens and focuses only on his math lessons.
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This is hella interesting when you have an English essay due
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imagine being a 1st grader doing their shapes homework and searches up “triangles” and gets this
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I needed this today. I’m building a house made entirely of Pythagorean Triples.
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Special Thanks to 1. Pythagoras 2.Reńe Descartes 3.Bernhard Riemann 4.Grant Sanderson For this Marvellous Video😄
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At some point you think you have seen everything, which is to say about a "simple" topic like pythagorean triples. And then comes this video and blows your mind with the elegance and simplicity of it all. And you will be reminded, there is no such thing as "simple topics" and "everything to know".
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"The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living.” - Henri Poincaré -
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치직... 한국인... 깃발 꼽고 경례..
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>has final exam in 2 days >*sees 3blue1brown uploaded new vid* >"the bloody exam can wait"
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I LOVE THE FACT THAT YOU ARE POSTING VIDEOS EVERY TIME PLEASE NEVER STOP
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What an amazing visualization. A few years back, I tried coming up with a proof to find an elegant proof for finding Pythagoras triplets. Didn’t succeed. But this video just gave me a whole new perspective. Cheers!
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You should make an ”Essence of topology” series. Topology is very visual but can be hard to describe with just numbers. I think ur animations would make a great fit for teaching topology You could cover topics like: Projective space, Equivalance relations or quotient space, affine geometry, hyperbolic geometry. And then u can end of the series by briefly giving an understanding to the poincaré conjecture.
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Absolutely beautiful! I have a Ph.D. in Mathematics and have never seen a discussion of Pythagorean Triples in terms of complex numbers before. Thanks for this great video!
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This is absolutely beautiful. Thank you so much for posting these videos. It is such a great pleasure to watch and learn the topics here with your incredible visuals to lead the way. I look forward to more amazing content in the future.
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I love how the students get angry when the teacher introduces complex numbers.
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Very grateful; just what I was looking for! Had a suspicion that Pythagorean Triples to All Triples were as Rational Numbers to All Real Numbers, but wondered how to get at showing it. Thank you for the missing clue of using the Complex Plane, and for the unusually clear and nicely paced presentation!
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This is quite simply the best Maths learning resource on the interent...a service to humanity!
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You have an incredible intuition and perspective on mathematics. Please never stop sharing your knowledge with us!
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I have a problem breathing every time I watch a 3b1b video because the concepts exposed there are breath-taking!!! Thank you Grant!
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Thanks a lot, great description, inspired video. Wow! The square of every integer pixels except those at diagonal go to Pythagorean triple. It shows us a fabric on how complex plane and complex number is defined.
