Posts Tagged ‘hypocycloid’

Let’s talk about the sine and cosine functions. One does not need to use very much information about these commonly seen functions in order to understand a large number of curves which can be drawn by graphing sine and cosine in Cartesian and polar coordinates. We will see sine curves, sums of sine curves, Lissajous figures, cycloids, hypocycloids, epicyclodes, and, of course, many rows of roses.

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Dr. Jonathan Kane will guide students through important theorems from “the results about angles in circles” to the “theory of inversion.”  He will then derive parametric equations for hypocycloids and similar curves.   Finally, the students will tackle many circle related problems which can be solved using these theorems.

Dr. Kane and Dr. Andreescu are the founders of the popular PurpleComet! problem solving contest.   Many people around the world have been talking about the paper authored by Dr. Kane and Dr. Janet Mertz, “Debunking Myths about Gender and Mathematics Performance.”  This follows another very popular paper by Kane, Mertz, Gallian and Andreescu called “Cross-Cultural Analysis of Students with Exceptional Talent in Mathematical Problem Solving.”

In these papers, Dr. Kane and his co-authors challenge the idea of a biological explanation for the difference in mathematical achievement by young men and women.  Instead they describe the many ways that cultural forces create a significant challenge to US students and particularly young women who would otherwise excel at mathematics and problem solving.  Certainly the outstanding performance of Lisa Sauermann at the International Mathematical Olympiad demonstrates this great potential.

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