How do we fit a three-dimensional world onto a two-dimensional canvas? Answering this question will change the way you look at the world. We'll learn where to stand as we view a painting so it pops off that two-dimensional canvas seemingly out into our three-dimensional space. We'll explore the mathematics behind perspective paintings, which starts with simple rules and will lead us into really lovely, really tricky puzzles. For example, why do artists use vanishing points? What's the difference between 1-point and 3-point perspective? Why don't your vacation pictures look as good as the mountains you photographed? Dust off those old similar triangles, and get ready to put them to new use in looking at art!
Annalisa Crannell is a Professor of Mathematics at Franklin & Marshall College and recipient, in 2008, of the MAA's Deborah and Franklin Tepper Haimo Award for Distinguished College or University Teaching of Mathematics. Her primary research is in topological dynamical systems (also known as "Chaos Theory"), but she also is active in developing materials on Mathematics and Art. Prof. Crannell has worked extensively with students and other teachers on writing in mathematics, and with recent doctorates on employment in mathematics. She especially enjoys talking to non-mathematicians who haven't (yet) learned where the most beautiful aspects of the subject lie.
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150 years ago B. Riemann discovered a pathway to understanding the prime numbers. But today we still have not completed his vision. I will give an introduction to Riemann's Hypothesis, one of the most compelling mathematics problems of all time, and describe some of its colorful history.
This talk explored some of the connections and analogies between mathematics and music in an attempt to explain why mathematicians tend to be musical.
Robots have been with us for only half a century, but the idea of man made mechanisms that can work and think goes back to ancient civilizations. The lecture presents the most important historical developments in robotics, emphasizing its interplay with mathematics. The first part of the lecture summarizes the pioneering work of Heron of Alexandria, Philo of Byzantium, Al-Jazari, Leonardo da Vinci, and other scientists up to the twentieth century. The second part is dedicated to artificial intelligence and the mathematical tools involved. The lecture concludes with the latest developments in robotics, and presents some open research problems in engineering, computer science, and mathematics, that need to be solved in order to fulfill the long standing promises of robotics.
Tiger Woods has an amazing record of winning golf tournaments. He has gained the persona of a player who is a winner, a player that when near the lead or in the lead can do whatever it takes to win. In this lecture I investigate whether in fact, he is a winner. A mathematical model is created for the ability of Tiger Woods, and all PGA Tour golfers to play 18 holes of tournament golf. The career of Tiger Woods is replayed using the mathematical model for all golfers and the results are very consistent with Tiger Woods’ actual career. The idealized Woods plays every hole the same, but with Woods’ natural variability from one hole to the next. This “Woods” plays no better or worse when he’s close to winning. Woods has not needed any additional winning dimension–only his pure golfing ability. So Woods is not a “winner” – but instead he is just a much better golfer than everyone else.