My grandchild raised an interesting problem related to geometry the other day. He was trying to find an area between circles that are sometimes called tangents, touching one another at a single point. I took a long time as I attended school and learned the geometry. So, I went to the Internet to find a solution. At first glance, it seems to be a fairly complicated problem since it involves partially curved areas. And the solution of the Internet supported this point by involving a solution of the equilateral triangle of the geometric center handling the curved area and some calculations.
While considering these solutions, I kept thinking there was a simpler way to find these areas. But I still can not quite see it. You know that your brain is looking at your brain to know you. A part of my brain said, "This one is better, it's easy! So after having starred this problem for a while, I finally realized the solution! I really surprised myself, It is that I could not find this simple solution anywhere on the net! I know it is there but I do not know where it is, so I think it's worth writing articles on solutions Perhaps, some university professors may find my solution wrong, but I do not think it is wrong.
Anyway, here is the answer. If you mark a circle inside the square (inside it) you will notice that the height and width of the square are equal to the diameter of the circle. Therefore simply subtract the area 3.14 x radius x or πR ^ 2 from the area of the circle (diameter of the square of the circle) and get the four small areas you are looking for! If you divide the answer by 4, you get one area of these small residuals.
(R 2 - PixR 2) / 4 = 0.215 R 2
Well, arrange any number of circles that touch each other, enclose it in boxes and count the small areas. For example, if four circles are in contact with each other, there are four small areas between them so simply multiply the solution of four small areas to get the total area between the circles. I think that I came out with 4 x 0.215 x R ^ 2 = 0.86 R ^ 2. It's simple.
I put this article on the net, and for the mathematics students and professors the old head on the block "Your head has gone wrong! Enjoy!
