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 36 Prove that $\prod_{k=1}^{n-1}\sin\frac{k \pi}{n} = \frac{n}{2^{n-1}}$ 6 How do you show that $d\theta = \frac{x dy - y dx }{x^2 + y^2}$? 5 Packing disjoint family of discs with radii $\tfrac{1}{2}, \tfrac{1}{3}, \tfrac{1}{4},\ldots$ inside the unit disc 5 Continuous function satisfying $f^{k}(x)=f(x^k)$ 4 Cutting the Cake Problem

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 +50 Prove that $\prod_{k=1}^{n-1}\sin\frac{k \pi}{n} = \frac{n}{2^{n-1}}$ +5 Matrix diagonalization theorems and counterexamples: reference-request. +10 Proof for the curl of a curl of a vector field +5 In which commutative algebras does any derivation possess a flow?

### Questions (8)

 17 Fundamental group of GL(n,C) is isomorphic to Z. How to learn to prove facts like this? 10 In which commutative algebras does any derivation possess a flow? 9 Matrix diagonalization theorems and counterexamples: reference-request. 8 Upper-triangular matrix is invertible iff its diagonal is invertible: C*-algebra case 5 Generalization of cos: is this function known?

### Tags (54)

 36 complex-numbers 6 differential-geometry × 3 36 products 6 calculus 36 roots-of-unity 5 functional-equations × 2 36 trigonometry 5 geometry 9 real-analysis × 3 5 puzzle

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