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Sum of Cubes as Sum of Odds and more (visual proof VI) 

Mathematical Visual Proofs
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This is a short, animated visual proof demonstrating two formulas for the sum of the first n positive cubes, one in terms of consecutive odd numbers and the other in terms of the square of a sum of consecutive positive integers. We end with a bonus visualization of a direct version of Nicomachus's theorem.
If you like this video, consider subscribing to the channel or consider buying me a coffee: www.buymeacoff.... Thanks!
Here are five other visual proofs of sum of cubes formulas:
• Sum Cubes with Triangl...
• Sum of Cubes IV (Nicom...
• Visual Sum of Cubes II
• Sum Of Cubes I (visual...
• Visual Sum of Cubes III
This animation is based on a visual proof by Alfinio Flores from the January 1998 issue of The College Mathematics Journal (www.jstor.org/... page 61).
To learn more about animating with manim, check out:
manim.community
#mathshorts​ #mathvideo​ #math​ #calculus #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #finitesums #discretemath #calculus #sum #induction

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14 окт 2024

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Комментарии : 13   
@soumyajitroy4783
@soumyajitroy4783 7 месяцев назад
Seriously a fantastic visual proof, have always been using that formula and knew the proof via mathematical induction but this is just eye opening
@MathVisualProofs
@MathVisualProofs 7 месяцев назад
You might like the others linked in the description too :) thanks!
@jakobthomsen1595
@jakobthomsen1595 7 месяцев назад
Wonderful!
@MathVisualProofs
@MathVisualProofs 7 месяцев назад
Thank you!
@TheMemesofDestruction
@TheMemesofDestruction 7 месяцев назад
Great Stuff! ^.^
@MathVisualProofs
@MathVisualProofs 7 месяцев назад
Thanks! 😄
@RobolsMath
@RobolsMath 6 месяцев назад
Also did a video a month ago but MVP’s version is definitely better. Hoping I improve in the future. 🥹 ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-wbxCrLGEmL8.htmlsi=ebS9a8hX3Nb0VCc_
@ryoikitokuiten
@ryoikitokuiten 7 месяцев назад
Hi. I've discovered visual proof of the integral of tanx = ln(secx). Where can I share it with you ?
@MathVisualProofs
@MathVisualProofs 7 месяцев назад
There is one in the literature and I have it in the pipeline to animate. Maybe it’s similar? I can find the source. But you can always email me.
@ryoikitokuiten
@ryoikitokuiten 7 месяцев назад
what is your email? I couldn't find it in your channel description.@@MathVisualProofs
@MathVisualProofs
@MathVisualProofs 7 месяцев назад
@@ryoikitokuiten I think you can only get it on desktop version of RU-vid maybe?
@ryoikitokuiten
@ryoikitokuiten 7 месяцев назад
I've sent an Email. @@MathVisualProofs
@Naej7
@Naej7 7 месяцев назад
WAT
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