My grandson was an interesting problem for me the other day when it came to geometry. He tried to find the area between the circles, which touch each other at separate points, sometimes called tangent circles. It has been a long time since I was in school, and the same thing for studying geometry, so I went to the Internet to find a solution. At first glance, this seems to be a rather complicated problem, since it involves partial curved areas. And the Internet solutions supported the point by showing a rather attractive geometric centered equilateral solution of a triangle with some calculus for processing curved regions.
While studying these solutions, I continued to think that there is an easier way to find these areas; but I just can't see it. You know how your brain sees things before you do it, and some part of my brain said, “Hey, dummy, do it like this, it will be easier!” So, after playing for some time this problem, I finally realized a quick fix! What really surprised me was that I did not find this easy solution anywhere on the net! I know it is there, but where it is, I have no idea. So, I thought it was worth writing an article about the solution. Maybe some college professor can show me what’s wrong with my decision, but I don’t see anything wrong with that.
Anyway, here is the answer. If you enter (place inside) a circle in a square, you will notice that the height and width of the square is equal to the diameter of the circle. So, just subtract the area of the circle equal to 3.14 to the radius of radius x or pi R ^ 2 from the area of the square (the diameter of the square of the square), and you will get four small areas that we are looking for! If you divide the answer into four, you will receive an area of one of these small residues.
(R ^ 2 - pi x R ^ 2) / 4 = 0,215R ^ 2
Now organize any number of circles touching each other and enclose them in squares to count small areas. For example, if you had four circles that touched each other, you would have four small areas between them, so just multiply our small solution by four, and now you will have the total area between the circles. I think I came out with 4 x 0.215xR ^ 2 = 0.86R ^ 2. Simple, isn't it.
I'm going to post this article online and my old head on the block, so that some mathematician or professor would say: “Hey, dummy, you messed up!” Have fun!
