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The generalization of determining the volume of a hypersphere in n-dimensions can be seen as a solution to the intriguing problem put forth by Grant Sanderson (@3blue1brown) in his video
*Why π is in the normal distribution (beyond integral tricks) Pi in Gaussian Integral* : https://www.youtube.com/watch?v=cy8r7WSuT1I
Chapters:
00:00 Need of Higher Dimensions
01:39 From 2D to Higher Dimensions
04:22 Generalization of a Factorial Function
08:59 Generalizing the Volume of a Hypersphere
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This video is animated using Manim library (based on Python).
Manim is an engine for precise programmatic animations, designed for creating explanatory math videos.
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