» 50 animals – rabbits and chickens – together at a length of 122 feet. How many rabbits and how many chickens? “
This question dates back to 1743 and is written on a wooden board in a Japanese temple. It was one of the many “sangaku” popular in Japan from the 17th to late 19th centuries. At that time, people would come up with such tablets containing mathematical problems as offerings, and puzzles to entertain pilgrims and encourage them to study mathematics.
This formula also belongs to sangaku:
It is necessary to prove the “Japanese theory”. The problem begins with a convex trigonometric polygon. This sounds a bit complicated, but it’s actually quite simple when you think about it.
A polygon is nothing more than a polygon. So you draw a few points – at least three – and connect them with straight lines, so that a closed line is created at the end. Triangles or squares are polygons. It can also run irregularly and consist of sides of unequal length. If the interior angles of a polygon are always less than 180 degrees, it is said to be convex.
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Now we need to triangulate the convex polygon. That is, we divide the area of \u200b\u200bthe polygon into triangles by connecting the lines between the points. If we then draw the circle in each of these triangles—the one that touches all sides from the inside exactly once—and sum up all of these radii, the result is always the same. It doesn’t matter which way the polygon is triangulated.
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