Norton's right. I made a mistake last time around and treated the second part of the problem as 2d.

Think everyone agrees that for the big sphere, distance of sphere to corner is (sqrt(3)-1)/2

This is equal to

distance of edge of big sphere to center of small sphere + distance of center of small sphere to corner

= r + r*sqrt(3) (the mistake i made last time was to say its r+r*sqrt(2))

so eq to solve is r(1 + sqrt(3)) = (sqrt(3)-1)/2

No! Because the smaller sphere never GOES THAT FAR...your value will be too big. Here's a picture. For people to reference.



Your method will produce the following image (not as pretty).



See the problem?

...I was in reply to PZ.

But, all we need is the small sphere's radius...so you don't use the small sphere's radius to find GH...you find GH to get the radius...no?

Can someone post the algebra they used in terms of that diagram?

If r is the small sphere's radius and 1/2 is the large sphere's radius:

DG = 2r
GH = r*sqrt(3) - r
DH = sqrt(3)/2 - 1/2

DG + GH = DH

I missed the thread before it got trashed, what was the original problem?

Lee

You have a cube with sides of 1, and a sphere inside with a diameter of 1. What is the largest sphere that can sit between the outer edge of the original sphere, and the inside edge of the cube.

Probably wrong but whatever:

How come you all are posting the cube as a square? If you take a cross section from one edge to the opposite edge, the cross section shape would be a rectangle (actually a 1 X sqrt(2) rectangle), not a square and the inner sphere would only be touching the top and bottom edges, and not the sides.

Which makes a lot of your assumptions wrong.

Equus, I think yours would be correct if the issue was to fit a cylinder across the box, but I don't think it's correct for the problem at hand.

Yea Mac...I think I see your point. You mean that if we take a diagonal cross section...from one edge of the cube to the opposite edge then we would get something like this:

And the other two edges would just be a vertical line right down the middle?

right

See, nortonesque, that isn't that hard to draw

I just redid it using the second image I posted and used the same equations in my first post. The angle I got (from the horizontal to a line from center to top corner) was 54.76 degrees and the length of a line from the center to a corner was .866.

The diameter for the small spheres were .268. Which is a little bigger than my first answer which makes sense.

EDIT: Nevermind...my bad drarwring skillz had the lines going through the center of the small spheres...when I draw it carefully I can see that the line from center of the big sphere to a corner does not pass through the center of the small spheres.

Like this:

My picture above isn't right I don't think. I think there would be a gap at each end between the small spheres and the edge of the cube...that way the diagonal line does pass through their center. So below is what I got...I skipped a bunch of math steps but the top 3 equations should be all you need.