# Category Archives: Extra

## What is Curvature? (II)

[ Background required: rudimentary vector calculus. ] The aforementioned definition of curvature is practical but a little aesthetically displeasing. Specifically, one seeks a definition which is independent of the parametrization of the curve. The advantage of such a definition is … Continue reading

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## What is Curvature? (I)

[ Background required: calculus, specifically differentiation. ] In this post, we will give a little background intuition on the definition of curvature. One possible approach is given in wikipedia, ours is another. Note that this is not IMO-related (my apologies … Continue reading

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## Pick’s Theorem and Some Interesting Applications

[ Background required: none. ] A lattice point on the cartesian plane is a point where both coordinates are integers. Let P be a polygon on the cartesian plane such that every vertex is a lattice point (we call it a lattice polygon). … Continue reading

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## Matrices and Linear Algebra

Background recommended : coordinate geometry Here I thought I’d give an outline of linear algebra and matrices starting from a more axiomatic viewpoint, instead of merely giving rules of computation – the way it’s usually taught in school. The materials … Continue reading