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Visual Proof for Sum of Squares Formula #SoME3
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#3b1b#manim#sum#proofs#SoME3#Gauss#VisualProofs#Sumofsquares
In this video, we show visual proof for the sum of powers of integers, for power 1 and power 2. This is my first manim video and put many hours of work into it in a constant effort to improve for my viewers and subscribers.
In this video you will hear a story about the genius of Gauss and will see beautiful geometrical proofs for the sums:
1+2+....+n=n(n+1)/2 and 1^2+2^2+...+n^2=n(n+1)(2n+1)/6.
The sum of the powers formula has an exceptionally beautiful geometric proof that involves the construction of a 3D puzzle that consists of 6 pieces.
To produce the videos on my channel I consume lots of coffee, you can help the channel by buying me a coffee:
Check out this great book that is all about visual proofs without words:
🔔 Click the bell in order not to miss new videos!
If you liked the lecture and the materials, any support on Patreon:
PayPal:
Visit the store to find cool items related to the channel, mathematics, physics
and engineering:
Shopping in the store is a great way to support the channel.
Check this cool shirt with the visual proof from the video printed on it.
You can be among the very few people in the world that have this unique custom-designed shirt.
Music Used with permission, license:
Creative Commons CC BY 3.0
I would also like to thank the Theorem of Beethoven for helping me with the preparation of the video and making a major part of the animation.
In this video, we show visual proof for the sum of powers of integers, for power 1 and power 2. This is my first manim video and put many hours of work into it in a constant effort to improve for my viewers and subscribers.
In this video you will hear a story about the genius of Gauss and will see beautiful geometrical proofs for the sums:
1+2+....+n=n(n+1)/2 and 1^2+2^2+...+n^2=n(n+1)(2n+1)/6.
The sum of the powers formula has an exceptionally beautiful geometric proof that involves the construction of a 3D puzzle that consists of 6 pieces.
To produce the videos on my channel I consume lots of coffee, you can help the channel by buying me a coffee:
Check out this great book that is all about visual proofs without words:
🔔 Click the bell in order not to miss new videos!
If you liked the lecture and the materials, any support on Patreon:
PayPal:
Visit the store to find cool items related to the channel, mathematics, physics
and engineering:
Shopping in the store is a great way to support the channel.
Check this cool shirt with the visual proof from the video printed on it.
You can be among the very few people in the world that have this unique custom-designed shirt.
Music Used with permission, license:
Creative Commons CC BY 3.0
I would also like to thank the Theorem of Beethoven for helping me with the preparation of the video and making a major part of the animation.
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