File:Geometric symmetry problem example.svg

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English: It is not immediately obvious what is the area of a small square inscribed in a circle, which itself is inscribed in a large square. However, by rotating the small square by 90° and then drawing the two diagonals of the small square, it becomes clear that the small square is composed of 4 identical triangles (red) and the large square of 8 identical triangles (blue and red), and therefore the small square has half the area of the large square. The use of the rotation symmetry operation simplifies the solution to the problem.
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Author GreatStellatedDodecahedron

Created using Wolfram Mathematica v14.3

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Problem: what is the area of a square inscribed in a circle, which itself is inscribed in a larger square? Solution: the small square has half the area of the large square.

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15 April 2026

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