creating circles from rectangles
August 17, 2008 6:49 AM Subscribe
Math filter: How many equally sized rectangles will fit into a circle, and how should I arrange them in order to make the best-looking approximation?
posted by brandnew to science & nature (9 answers total) 2 users marked this as a favorite
I want to create an approximate circle from a number of equally-sized rectangles. How do I do this for an arbitrarily sized rectangle or circle?
For example, suppose I have 100 rectangles of size 5x6 (or generally LxW). I want to create the best approximation of a circle using these rectangles. How can I calculate what the resulting radius of the circle will be, and how do I arrange the rectangles to achieve the best approximation?
The inverse question is also useful: If I want to create an approximate circle with a radius of 31, how many rectangles of size 5x6 (or LxW) do I need, and how should I arrange them?
The general formula / strategy / algorithm would be most useful. But, if you have the answer for 100 rectangles of size 5x6, that would be good too. I'm also interested in the answering the same question for 25-30 rectangles of size 11x11.