- 03 Oct '03 15:55Draw a square. Draw inside the square the largest circle that'll fit. Draw between the circle and the square the largest circle that'll fit. What is the ratio between the radii of the two circles?

(Once again, there's not a lot of point in mathematicians answering this, as it's not very hard. I can't think of any to trouble the likes of RC ) - 03 Oct '03 19:33

The way you've described it, the first circle would just touch the sides of the square, leaving no room for a second circle between it and the square. Perhaps you could rephrase your question?*Originally posted by Acolyte***Draw a square. Draw inside the square the largest circle that'll fit. Draw between the circle and the square the largest circle that'll fit. What is the ratio between the radii of the two circles?**

(Once again, there's not a lot of point in mathematicians answering this, as it's not very hard. I can't think of any to trouble the likes of RC ) - 03 Oct '03 20:14
*Originally posted by Acolyte***Draw a square. Draw inside the square the largest circle that'll fit. Draw between the circle and the square the largest circle that'll fit. What is the ratio between the radii of the two circles?**

(Once again, there's not a lot of point in mathematicians answering this, as it's not very hard. I can't think of any to trouble the likes of RC )

1:2 - 03 Oct '03 20:40

Look at my avatar: the second circle has to fit in the grey area.*Originally posted by richjohnson***The way you've described it, the first circle would just touch the sides of the square, leaving no room for a second circle between it and the square. Perhaps you could rephrase your question?** - 12 Oct '03 19:08

Square with sides 2, so the biggest circle in it has radius 1. On the diagonal of the square there is exactly sqrt(2)-1 left in the top left corner. The bit is the diagonal of a smaller square, with sides...sqrt(3/2 - sqrt(2)). So the cicle in there would have radius 1/2*sqrt(3/2 - sqrt(2)), wich is then the ratio of them.*Originally posted by Acolyte*

(Once again, there's not a lot of point in mathematicians answering this, as it's not very hard. I can't think of any to trouble the likes of RC )

Wich is also sqrt(2) / sqrt(3 - 2*sqrt(2)) : 1

I think... - 13 Oct '03 14:36

Hmm, I don't see what you're doing, but ....*Originally posted by TheMaster37***Square with sides 2, so the biggest circle in it has radius 1. On the diagonal of the square there is exactly sqrt(2)-1 left in the top left corner. The bit is the diagonal of a smaller square, with sides...sqrt(3/2 - sqrt(2)). So the cicle in there would have radius 1/2*sqrt(3/2 - sqrt(2)), wich is then the ratio of them.**

Wich is also sqrt(2) / sqrt(3 - 2*sqrt(2)) : 1

I think...

The answer is:

sqrt(2)-1 : sqrt(2)+1

Perhaps you might think now: WHY? so I'll give you my reasoning.

The ratio of the radii equals the ratio of the (2*radius+distance from circle to corner of the smallest square around the circle)s. These lengths are easy to compute. The numbers in the answer are those lengths if you start with a square with sides 2. - 13 Oct '03 16:42

That small circle won't fit inside the square if you use the distance from the circle to the corner as the diameter.....*Originally posted by Fiathahel***Hmm, I don't see what you're doing, but ....**

The answer is:

sqrt(2)-1 : sqrt(2)+1

Perhaps you might think now: WHY? so I'll give you my reasoning.

The ratio of the radii equals the ratio of the (2*radius+distance from circle to corner of the smallest square around the circle)s. These lengths are easy to compute. The numbers in the answer are those lengths if you start with a square with sides 2.

P