A Mathematical Coincidence
Take any Kepler triangle with sides and consider:
- the circle that circumscribes it, and
- a square with side equal to the middle-sized edge of the triangle.
Then the perimeters of the square and the circle coincide up to an error less than 0.1%.
This is the mathematical coincidence . The square and the circle cannot have exactly the same perimeter, because in that case one would be able to solve the classical (impossible) problem of the quadrature of the circle. In other words, because is a transcendental number.
According to some sources, Kepler triangles appear in the design of Egyptian pyramids. However, the ancient Egyptians probably did not know the mathematical coincidence involving the number and the golden ratio .
Read more about this topic: Kepler Triangle
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