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Curated by: Mathematical Visual Proofs (650 videos)
Summing odds via area This is a short, animated visual proof showing one method to find the sum of the first n odd positive integers decomposing an array of unit squares into rectangular and triangular pieces and using area formulas for those pieces. If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! To see the other methods for finding the sum odd integers visually, check out the following videos: https://youtu.be/jq5AYCgkciE?si=U6bxLBmWjyBD_HQZ https://youtu.be/I4A2T55k0cg https://youtu.be/x3qfFBNRRDg https://youtu.be/ZeEOgbLo0Rg https://youtu.be/6H6nCpGW1nU For other sums related to odd integers, check out these visuals: https://youtu.be/WKxoi2i0EaE (summing odd squares) https://studio.youtube.com/video/9BC1klE8jMk/edit (alternating odd sums) https://youtu.be/MmOTqrtbtFQ (odd sum ratios) https://youtu.be/fTBvVeURb3Q (odd sum ratios II) This animation is based on a visual proof due to Samuel G. Moreno that appeared in the October 2017 issue of Mathematics Magazine (https://doi.org/10.4169/math.mag.90.4.298 page 298). #manim #math #proofwithoutwords #visualproof #squarenumbers #oddnumbers To learn more about animating with manim, check out: https://manim.community