We are a group of mathematics students in the Chinese University of Hong Kong.

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 Why is a² + b² ≥ 2ab ?
 A remark on the divergence theorem
 The CauchySchwarz inequality and the Lagrange identity
 On the existence of a metric compatible with a given connection
 A curious identity on the median triangle
 27 lines on a smooth cubic surface
 Weighted HsiungMinkowski formulas and rigidity of umbilic hypersurfaces
 The discrete GaussBonnet theorem
 Why a vector field rotates about its curl?
 A functional inequality on the boundary of static manifolds
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 Mean value properties for harmonic functions on Riemannian manifolds
 A note on Obata's theorem
 Mathematics behind JPEG
 Understanding Lagrange multipliers (1)
 The BrunnMinkowski inequality and the isoperimetric inequality
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 Why does a mirror reverse left and right, but not top and bottom?
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想左一個好廢的 COROLLARY
Every countable set must has a proper countable subset that is bijective to it
but how many of such subset
how many means cardinality …