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Volume of a ball in n dimensions

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Dr Peyam

In this video I explicitly calculate the volume of a ball of radius r in R^n. The method I’m presenting uses only multivariable calculus and the disk method from singlevariable calculus, but we’ll also visit some other goodies like the Beta function and the Gamma function. Enjoy!

posted by chan5g2imb


Surface area of sphere in n dimensions
Surface area of sphere in n dimensions
The Weak Derivative
The Weak Derivative
Imaginary derivative of x
Imaginary derivative of x
How to derive the volume of an ndimensional hypersphere (the long version)
How to derive the volume of an ndimensional hypersphere (the long version)
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Strange Spheres in Higher Dimensions Numberphile
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Tesseract Hypercube 4th dimension Infinity Mirror Art Sculpture by Nicky Alice
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The Volume of a Sphere Numberphile
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Calculus of Variations
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Drawing the 4th, 5th, 6th, and 7th dimension
Drawing the 4th, 5th, 6th, and 7th dimension
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So why do the volumes of all even dimensional unit spheres sum to e^π?
A tesseract visualized
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The Volume of Balls in n dimensional Euclidean Space
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