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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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Category Archives: Combinatorics
The discrete GaussBonnet theorem
This is a slight extension of my previous note on discrete GaussBonnet theorem. As mentioned in that note, this is a generalization of the wellknown fact that the sum of the exterior angles of a polygon is always , which … Continue reading
Posted in Calculus, Combinatorics, Discrete Mathematics, Geometry, Topology
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Toric perspective 1
This series of posts will be about toric varieties. The author is not sure if there is a part 2, but he still calls this part 1. This post is about computing the dimensions and degrees of popular toric varieties. … Continue reading
Posted in Algebraic geometry, Combinatorics
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A Fibonaccilike sequence
What’s the pattern of the following sequence? Can you guess the next term? The answer is
Posted in Algebra, Combinatorics
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Some thoughts on 1+2+3+…
This post is a rather dumb one – and, contrary to the title, the emphasis is not on . In fact, I just put some of my dumb thoughts here after reading a comment of Terry Tao in his own … Continue reading
Posted in Combinatorics
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