/sci/ - Science & Math » Thread #11487618

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Anonymous Sat 21 Mar 00:31:40 2020 No.11487618 View Reply Original Report

Quoted By: >>11487622 >>11487639 >>11487652 >>11487960

Besides the stupid integral explanation of the volume formula, why, GEOMETRICALLY, is the volume of any pyramid or cone exactly one third the volume of the prism or cylinder with the same base and height? Other than taking the formula as gospel it makes no sense at all.

Anonymous

Anonymous Sat 21 Mar 2020 00:34:27 No.11487622 Report

Quoted By: >>11487638

>>11487618
would you accept a derivation of the formula?

Anonymous

Anonymous Sat 21 Mar 2020 00:42:06 No.11487638 Report

Quoted By: >>11487728

>>11487622
Nope. I've already gone through said derivation many times. I just keep coming back to this because it's so unintuitive.

Anonymous

Anonymous Sat 21 Mar 2020 00:42:11 No.11487639 Report

Quoted By: >>11487652

>>11487618
the average cross-sectional area is a third of the base
cross-section for pyramids of height x scales with x^2
the average value of x^2 over some interval from 0 to b is b^2/3

new

new Sat 21 Mar 2020 00:45:16 No.11487652 Report

Quoted By:

>>11487618
basically OP>>11487639 this guy is right. The integral is a form of averaged multipication, if you don't understand it you just need to get a better intuition for integrals and how they apply to geometry

Anonymous

Anonymous Sat 21 Mar 2020 01:08:05 No.11487728 Report

Quoted By: >>11487946

>>11487638
It doesnt fucking matter if its unintuitive. Is it logically sound? What a stupid thread

Anonymous

Anonymous Sat 21 Mar 2020 02:29:29 No.11487946 Report

Quoted By: >>11488038

>>11487728
A direct geometric proof must be possible. But is there a simple one?

Anonymous

Anonymous Sat 21 Mar 2020 02:35:03 No.11487960 Report

Quoted By:

>>11487618
Proposition 7, Book 12.
Euclid, read it.

Anonymous

Anonymous Sat 21 Mar 2020 03:08:29 No.11488038 Report

Quoted By:

>>11487946
https://mathcs.clarku.edu/~djoyce/java/elements/bookXII/propXII7.html#cor

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