bob012345's latest activity

That is until someone falls into a black hole and gets spaghettified.

Suppose any two volumes with one properly contained within the other. As the number of dimensions increases the relative volume of the...

Ah yes, of course - obvious once you point it out.

Possibly related and interesting: 3Blue1Brown (YouTube) - Thinking outside the 10-dimensional box 3Blue1Brown (YouTube) - The most...

desmos.com/3d/ky3el7b8v7

Consider a sphere and cube with the same center and volume. As the number of dimensions increases the volume of their intersection goes...

At the time I couldn’t figure out how to make Latex to do ##\approx##. Now I do and I edited the above post. Thanks. Regarding...

Looking at a projection of the 3D case we can see how the ball is smaller for the same ##R##.

I got the same as #3.

Here is the next part; In the case of 4D, ##d=\sqrt{4}r=2r## then ##r=\frac{R}{3}##. In the general case ##d=\sqrt{n}r## and the ratio...

Here is the first part; Let the center to center distance be ##d## and ##r## the smaller circle radius and ##R## the larger circle...

Here is an interesting geometry problem given for general interest. In the figure, compute the fraction that is shaded. Then extend that...

If it isn't simpler, it certainly is more elegant.

I don’t know if this is simpler but it can be done as the intersection of a line and a circle. Note, I’m using ##x## as the standard...

Thanks @Gavran for pointing out those cases. In my formulation, I computed the largest petal and the next largest petal which accounts...