Proof Without Words #2

My last post seemed to go down well so I thought I’d compile a few more images of proofs without words!

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Determinant is the area of a parallelogram, by Solomon Golomb, Mathematics Magazine, March 1985.

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Jensen_graph.png

A visual proof of Jensen’s inequality, found on Wikipedia. Jensen’s inequality states that

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In the diagram, the dashed curve along the X axis is the hypothetical distribution of X, while the dashed curve along the Y axis is the corresponding distribution of Y values. Note that the convex mapping Y(X) increasingly “stretches” the distribution for increasing values of X.

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Hope you enjoyed! M x

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