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.

## Archive for January, 2013

## February 2, 2013 – Dr. Branislav Kisačanin – “A Tour of Mathematical Functions”

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| 1 Comment »

## January 26, 2013 – Dr. Jonathan Kane – “Constructions with Straight Edge and Compass and Other Implements”

Posted in meeting, tagged AIME, AwesomeMath, compass, constructions, geometry, Jonathan Kane, math circles, Purple Comet on January 20, 2013| Leave a Comment »

Learn all about the classic theory of geometric objects with only straight edge and compass. What can you construct, and what is impossible? Which regular polygons can you construct? What if you have help by being given a fixed parabola? Come with your pencils and be ready to draw (compasses provided, or bring your own)!

To perform well on geometry problems on math competitions it is necessary to have a deep understanding. This understanding can be achieved by retracing the footprints of the very first mathematicians whose only tools were a straight edge and compass.

Dr. Kane is one of our most popular lecturers and is recently retired from his position as a professor at the University of Wisconsin – Whitewater. Along with Dr. Andreescu he is the co-founder and coordinator of the Purple Comet! Math Meet. Dr. Kane is also the co-chair of the AIME committee and a faculty member at the AwesomeMath summer camp.

Along with his wife, Jane E. Mertz, Jonathan Kane is the author of several important research papers on the role of culture and gender in mathematical achievement including “Debunking Myths about Gender and Mathematics Performance.”

## January 19, 2013 – Ivan Borsenco – “Exploring the world of Probability”

Posted in math circle, meeting, tagged IMO, Ivan Borsenco, math circles, MIT on January 14, 2013| 2 Comments »

MIT student and four time International Mathematical Olympiad participant, Ivan Borsenco, will return to the Metroplex Math Circle this week!

Ivan will introduce the classical probability theory. There will be many interesting examples and several unexpected results. Students will solve a few mathematical paradoxes, find out how to build simple probabilistic models, and have lots of fun.

A deep understanding of probability is not only useful for contest preparation, but is critical for anyone planning a career in science or business.