Sum of Cubes as Sum of Odds and more (visual proof VI)
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- Опубліковано 1 бер 2024
- 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.buymeacoffee.com/VisualPr.... 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/stable/2687639 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
Seriously a fantastic visual proof, have always been using that formula and knew the proof via mathematical induction but this is just eye opening
You might like the others linked in the description too :) thanks!
Wonderful!
Thank you!
Great Stuff! ^.^
Thanks! 😄
WAT
Also did a video a month ago but MVP’s version is definitely better. Hoping I improve in the future. 🥹
ua-cam.com/video/wbxCrLGEmL8/v-deo.htmlsi=ebS9a8hX3Nb0VCc_
Hi. I've discovered visual proof of the integral of tanx = ln(secx). Where can I share it with you ?
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.
what is your email? I couldn't find it in your channel description.@@MathVisualProofs
@@ryoikitokuiten I think you can only get it on desktop version of UA-cam maybe?
I've sent an Email. @@MathVisualProofs