Graduate Proofs
Proofs written during graduate study in mathematics.
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Proof The Reflective Property of the Ellipse
The normal to an ellipse bisects the focal angle: a gradient proof and Heron's shortest-path proof.
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Proof Three Tangents to a Parabola
Two tangents to any parabola are cut by a third in ratios summing to one, via similarity to y = x^2.
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Proof Varignon's Theorem
The midpoints of any quadrilateral form a parallelogram with half its area, by one line of vector algebra.