Re: 4 large dimensions

Posted by DickT on July 23, 19101 at 07:33:37:

In Reply to: Re: 4 large dimensions posted by Cooper on July 23, 19101 at 04:07:46:

I thought of an easier way. Consider any 2_d (plane) section throught the center of the 4-ball. Define an angular measure theta on the circumference of the section and note that the radius of a generic 3-ball satisfies r = cos theta by elementary trig.

Now integrate d_Vol = (4/3) pi (cos theta)³ d_theta
from theta = 0 to theta = pi/2 (gets all 3-balls in upper half of 4-ball) and then multiply by 2. The integral is easy (break it up).

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Follow Ups: (Reload page to see most recent)

• Re: 4 large dimensions -- AlexanderS1 7/25/101 (2)
  • Re: 4 large dimensions -- AlexanderS1 7/25/101 (1)
    • Further corrections -- AlexanderS1 7/26/101 (0)
• General Case -- DickT 7/23/101 (0)

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