AIM Math Teachers’ Circle – San Jose
Every month from September to April (except December), the AIM Math Teachers’ Circle will offer meetings for math teachers interested in exploring accessible, exciting topics in mathematics and learning about a problem-solving approach to teaching math. Meetings are also held on selected Saturday mornings. Meetings include lunch or dinner, which is complimentary.
We’ll make some beautiful conjectures – some of which might be totally false. Then we’ll celebrate the human gift of erring and come up with some more conjectures. Let’s remove the stigma of failure from the classroom by celebrating false conjectures and interesting errors. Mathematics should be physically beautiful. Engage an extra 10-20% of students by keeping things beautiful.
American Institute of Mathematics, 600 E. Brokaw Rd., San Jose, CA 95112. We are on the second floor of the Fry’s Electronics Home Office (on the other side of the building from the Fry’s store entrance). You can park anywhere in the Fry’s lot adjacent to Brokaw Rd.
Sonya Kohli, American Institute of Mathematics, skohli (at) aimath . org
Brian Conrey, American Institute of Mathematics
Tom Davis, San Jose Math Circle
Mary Fay-Zenk, Miller Middle School (retired)
Tatiana Shubin, San Jose State University
Josh Zucker, Julia Robinson Mathematics Festival
Session leader: Brian Conrad
Session topic: Pythagorean Triples and Conics
Among the solutions to the Pythagorean equation in whole numbers, some examples such as (3,4,5) and (5,12,13) are generally familiar (and perhaps (8,15,17) is to a lesser extent). Are there infinitely many such triples if we disregard the operation of scaling (e.g., creating (6,8,10) from (3,4,5))? The answer is affirmative in a definitive way: there is a nifty explicit formula that generates all such examples in terms of 2 parameters.
But much more remarkable than the purely algebraic fact of such a formula is that it has an elegant geometric explanation that is the tip of the iceberg on getting geometric insight into variations of the Pythagorean equation (involving ellipses and hyperbolas). This will provide a hands-on introduction to some basic ideas in the fascinating subject of algebraic geometry.
American Institute of Mathematics
600 E Brokaw Rd, San Jose, CA 95112