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143 : true
46,756 Views ⢠Apr 23, 2023 ⢠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!
Here is a longer version of this proof :    â˘Â Sum of Cubes IV (Nicomachus's Theorem) Â
Here are three other visual proofs of sum of cubes formulas:
   â˘Â Visual Sum of Cubes II Â
   â˘Â Sum Of Cubes I (visual proof) Â
   â˘Â Visual Sum of Cubes III Â
This animation is based on independently discovered, separate visual proofs by J. Barry Love from the March 1977 issue of Mathematics Magazine (www.jstor.org/stable/2689727), page 74, and Alan L. Fry from the January 1985 issue of Mathematics Magazine (www.jstor.org/stable/2690228) , page 11.
This is my version of a classic visual proof. Here are other renditions:
   â˘Â Nicomachus's theorem | Visualisation ...  by @ThinkTwiceLtu
   â˘Â Nicomachus's theorem | visual proof |...  by @Mathocube
   â˘Â Animating Nicomachus's 2000 year old ...  by @Mathologer
#mathshortsâ #mathvideoâ #mathâ #calculus #mtbosâ #manimâ #animationâ #theoremâ #pwwâ #proofwithoutwordsâ #visualproofâ #proofâ #iteachmath #finitesums #discretemath #calculus #sum #induction
To learn more about animating with manim, check out:
manim.community/
Views : 46,756
Genre: Education
Date of upload: Apr 23, 2023 ^^
Rating : 4.969 (35/4,457 LTDR)
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User score: 98.83- Overwhelmingly Positive
RYD date created : 2024-06-22T03:14:10.406328Z
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YouTube Comments - 48 Comments
Top Comments of this video!! :3
Math never gets old! Even ancient math.
74 |
Its also kinda a fun prank to play. Cuz we always say (a+b)^nâ a^n+b^n, but we can say (1+2+3+âŚ+n)^2 and âpretendâ to distribute the power improperly but change the power 2 to power 3
25 |
As always the best channels on YouTube are underrated and don't get enough attentionđ˘ hidden gems
10 |
This is a mind blowing concept
30 |
How... did I never know this? I work with numbers all the time. Damn. đ¤Ż
9 |
Waaw... i wondered the proof of this many tyms, here its explained as simple as possible... lovely...
1 |
I do like these videos.... most of it stuff I already know but the visual explanation is so easy to digest.... I'm a little jealous of my daughter getting to learn maths with videos like this teaching her not just rules but showing how those rules come about and so why they work for evry number .... if they don't use videos like this at her school then I'll use them at home.
Thank you for the time and effort you put into making these animations
1 |
Excellent đ
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Love the math demonstrations, keep up the posts â¤
1 |
So your saying that 1 plus the smallest cubed number and it doesn't work if you don't put the cubes in order and it only works with all the cube numbers between the biggest and the smallest?
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I think I love you
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Beautiful video. What software do you use to animate the cubes like that?
2 |
Hey! Can you do a visual proof for Euler's Identity?
1 |
Very nice. Ancient Greeks were smart.
1 |
Could you do a video on finding very large primes
3 |
The 4 numbers lived in harmony and peace, but everything changed when the ăEă attacked.
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I wonder if it also is true that
ÎŁ (n^4) from 0 to â = (ÎŁ (n))^3 from 0 to â
1 |
Could this be considered as a valid mathematical proof ?
1 |
Can you do an easy way to calculate pi please?
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@enescoskun0123
1 year ago
The total area is (1+2+3...n)² and because (1+2+3...n) equals n²+n / 2, the formula is n²(n+1)²/4
93 |