Basel's Problem
1+\frac{1}{4}+\frac{1}{9}+\cdots = \sum_{n=1}^{\infty}\frac{1}{n^2}=\frac{\pi ^2}{6}
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Viviani's Theorem
Viviani's Theorem states that for any point \mathcal{P} inside an equilateral triangle \mathcal{ABC} the sum of the lengths of perpendiculars drawn from P on the sides is equal to the length of the altitude. Draw equilateral triangles from that point onto the sides of the triangle such that these 3 perpendiculars are the altitudes of the equialteral triangles.Now rotate the triangles as shown.Now it can be easily seen that the sum of the 3 perpendiculars=perpendicular of the \Delta ABC
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