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Sum of Odd Cubes is Triangular (visual proof without words) 

Mathematical Visual Proofs
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This is a short, animated visual proof of the formula that computes that sum of the first n odd cubes by representing cubes as n copies of an nxn array.
If you like this video, consider subscribing to the channel or consider buying me a coffee: www.buymeacoff.... Thanks!
Here are some related visual proofs about the sum formulas:
• 3D Visual Sum of Odd S...
• Sum of Cubes as Sum of...
• Sum Cubes with Triangl...
• Sum of Cubes IV (Nicom...
• Visual Sum of Cubes III
• Visual Sum of Cubes II
• Sum Of Cubes I (visual...
This animation is based on a visual proof by Monte J. Zerger from the December 1995 issue of Mathematics Magazine (www.jstor.org/... page 371).
#math #manim​ #mathvideo​​ #sumofcubes​ #oddcubes #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #finitesums #discretemath #sum #induction #triangularnumbers #triangles
To learn more about animating with manim, check out:
manim.community
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14 окт 2024

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Комментарии : 21   
@alanthayer8797
@alanthayer8797 6 месяцев назад
Great visuals as usual I watchm all
@MathVisualProofs
@MathVisualProofs 6 месяцев назад
Much appreciated!
@ajinkya3.14
@ajinkya3.14 6 месяцев назад
That's quality!
@math_travel
@math_travel 6 месяцев назад
it's amazing and beautiful. thanks!
@MathVisualProofs
@MathVisualProofs 6 месяцев назад
Glad you like it! Thanks for watching!
@wyattstevens8574
@wyattstevens8574 6 месяцев назад
Neat! I knew the opposite would work at least for Mersenne-prime indices!
@MathVisualProofs
@MathVisualProofs 6 месяцев назад
😎
@BillGreenAZ
@BillGreenAZ 6 месяцев назад
This is the most clever one I've ever seen!
@MathVisualProofs
@MathVisualProofs 6 месяцев назад
😀👍
@tuanhungang5621
@tuanhungang5621 6 месяцев назад
thank you so much , i watched all your videos ,hope you upload more
@MathVisualProofs
@MathVisualProofs 6 месяцев назад
Thanks for checking them out!
@coder436
@coder436 6 месяцев назад
Fun fact: the sum of consecutive odd numbers is always a square
@MathVisualProofs
@MathVisualProofs 6 месяцев назад
Got that on my channel in several visuals :)
@braydentaylor4639
@braydentaylor4639 6 месяцев назад
Only if you start with 1
@robin9740
@robin9740 6 месяцев назад
​@@braydentaylor4639 which is odd
@braydentaylor4639
@braydentaylor4639 6 месяцев назад
@@robin9740 Yes. One is an odd number.
@rafiihsanalfathin9479
@rafiihsanalfathin9479 6 месяцев назад
@@robin9740the point he is making is if you start with 5 for example it doesn’t work
@almawizard1013
@almawizard1013 6 месяцев назад
What app do you do it with?
@MathVisualProofs
@MathVisualProofs 6 месяцев назад
I use 3blue1brown's python animation library called manim.
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