Posted in math circles, meeting, tagged AMC 10, AMC 12, Archimedes, brachistochrone, Branislav Kisacanin, cardioid, catenary, cicloid, circle, ellipses, euler, exponential functions, hyperbolas, hyperbolic functions, logarithmic functions, Newton, parabolas, tautochrone, trigonometric functions on January 27, 2013|
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Parabola or catenary?

In this lecture we will retrace the steps of Archimedes, Newton, Euler, and other great mathematicians and learn about important mathematical functions, their properties, history, and applications. We will look at several interesting competition topics that often show up on AMC 10/12, related to exponential, logarithmic, trigonometric, hyperbolic, and other functions. We will also see how these functions turn up in solutions of some fundamental problems in math, physics, and engineering. We will have fun using them to draw important curves: cicloids, cardioids, catenaries, circles, ellipses, hyperbolas, parabolas, and will discover which one of them is brachistochrone and which one is tautochrone.

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