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How was built the polygon polygon?

For modern student is not difficult to construct a regular polygon. Everyone can draw a triangle, square, Pentagon... Even if the number of parties increases to several tens, the solution will require just a little more patience and perseverance. But what to do when it comes to thousands and tens of thousands of parties?

In the German University town of göttingen has been one of those curious. Told about him famous English mathematician D. Littlewood. One is not a measure of obsessive student brought his head out of patience. Wanting a little rest from the meticulous student, the Professor said to him: "Go and develop the construction of correct polygon with 65 357 parties".

Professor long got rid of the pupil, because diligent German took the job of head seriously. He returned 20 years later with the appropriate building. And now this miracle perseverance is stored in the archives at the University of göttingen.

Other sources say that this story is just a joke invented by Littledog based on real events: the building actually exists and the original is actually stored in the library at the University of göttingen. This build has made the mathematician Johann Gustav Hermes in 1894, spending more than 10 years. The manuscript is more than 200 pages contained in the huge suitcases and because of its immense size was never published.

By the way...

Why 65 537 parties? Of course, the Professor took it from the ceiling. The fact that in 1836, the famous German mathematician Carl Friedrich Gauss proved that a regular polygon can be constructed using only a compass and straightedge, if the number of vertices is equal to the simple number of the Farm, i.e. the number of views , where n is a nonnegative integer.

And 65 537 is the largest known number Farm:

So how is this miracle of human thought - shestidesyatipyatiletnego? It looks almost indistinguishable from a circle! Because of its Central angle, i.e. the angle with the vertex in the center of the circle, is negligible - 0°0'19"77508888. If you draw 65537-gon with the length of one side of 1 cm, the diameter is more than 200 meters


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