It proves a number of interesting inequalities; for example, of all triangles with the same perimeter, the equilateral triangle has the greatest area; of all quadrilaterals with a given area, the square has least perimeter; and the famous Steiner theorem, the circle has . Bernouilli's Inequality. Consider the following statement: a > 0, f3 > 0, n ~ 1 ===}. an. --> na-(n-1)[3· {3n-1 - '. and the two sides are equal only if either n = 1 or a = [3. (1) Here, as throughout, we are making statements about real numbers, and in addition we require n to be a positive integer. Cambridge Core - Geometry and Topology - Geometric Inequalities - by Nicholas D. Kazarinoff Skip to main content We use cookies to distinguish you from other users and to provide you with a better experience on our websites.

# Geometric inequalities kazarinoff firefox

Luke Robitaille Geometric Inequalities Part 2 of 3, time: 13:57

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