bob012345's latest activity

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...

The formula ## f=(\pi/5+\sin72^\circ/2-2\sin72^\circ\sin^236^\circ)/(\pi/5+\sin72^\circ/2)\\ ## from post #6 can be transformed into a...

I worked up the general case for integer ##n## overlapping circles. Here is the Desmos page; The red circle is the generator of the...

My answer was actually <0.4 at about 0.3974 so I am investigating my math… EDIT: I did the calculation another way and agree with @Gavran.