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Sum of Odd Cubes is Triangular (visual proof without words)
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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.
Here are some related visual proofs about the sum formulas:
#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:
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Music in this video:
Creative Commons / Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0)
Here are some related visual proofs about the sum formulas:
#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:
_______________________
Music in this video:
Creative Commons / Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0)
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Sum of Odd Cubes is Triangular (visual proof without words)
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