4
votes
1answer
44 views

Does an infinite collection of circles accumulates at a circle?

There is an infinite collection of closed circles in the plane, all within a finite bounding square. Does it contain an infinite sequence of circles that converge to a circle? Assume that a point is ...
3
votes
3answers
183 views

Infinite series of tangential circles?

I want to show that for all $n$ there is some collection of $n + 2$ circles such that two of the circles ($A$ and $B$) are tangential to each of the remaining $n$ circles (but not to each other) and ...
6
votes
2answers
112 views

Circle Chord Sequence

This is my first post, so be nice! When I was in my first Geometry class in high school, I asked the teacher the following: Given a circle of radius 2a, find the length of the chord running parallel ...
7
votes
1answer
668 views

How to turn this sum into an integral?

I have been trying to find the closed form of this sum to no avail. It was suggested to me to try and turn this sum into an integral and solve it like that. However, I am confused as to how to do ...
2
votes
1answer
254 views

Convergence and closed form of this infinite series?

If we have a circle of radius $r$ with an $n$-gon inscribed within this circle (i.e. with the same circumradius), we can find the difference of the areas using: $$A_n =\overbrace{\pi r^2}^\text{Area ...
-1
votes
1answer
177 views

How to find the area. Linked with another question. [duplicate]

Possible Duplicate: Is value of $\pi = 4$? In this question we discussed why the fake proof is wrong. But, what about the area? The process converges to the same area of the circle ...
3
votes
1answer
134 views

summing series using circles inside curves

After watching the infinity elephants video http://www.youtube.com/watch?v=DK5Z709J2eo and seeing how a geometric series could be represented by drawing a circle between a pair of lines, then the ...