Jensen: the master key to many classic inequalities. скачать в хорошем качестве

Jensen: the master key to many classic inequalities.

It's amazing how many important results follow from Jensen's inequality! Many of the classic results about arithmetic, geometric and harmonic means follow from Jensen's. In this video we also prove the N-way Jensen inequality using the convex polygon centroid theorem. Convex functions, convex polygon theorem and division of segments.    • Fun with convex functions.      • Centroids of convex polygons.      • Leonardo da Vinci's ellipse-drawing d...   Proof of N-way AM-GM by algebra and induction:    • The precursor to AM-GM.      • AM-GM inequality proof and mean-power...