# BATMATH

**Bay Area Teachers and Mathematicians**

## Math Teachers’ Circles

## AIM Math Teachers’ Circle – San Jose

## Monterey County Math Teachers’ Circle

## San Francisco Math Teachers’ Circle

## Wine Country Math Teachers’ Circle

## AIM Math Teachers’ Circle – Stanford

## Morgan Hill Math Teachers’ Circle

## San Joaquin Math Teachers’ Circle

## Hollister Math Teachers' Circle

## East Bay Math Teachers’ Circle

## San Benito County Math Talks

## Santa Cruz Math Teachers’ Circle

### San Benito County Office of Education

460 5th St, Hollister, CA 95023

### Sonoma County Office of Education

5340 Skylane Blvd, Santa Rosa, CA 95403

### Sonoma State University

1801 E Cotati Ave, Rohnert Park, CA 94928

### MBAMP - Math Department UC Santa Cruz

1156 High St, Santa Cruz, CA 95064

### San Joaquin County Office of Education

2922 Transworld Dr, Stockton, CA 95206

### Proof School

555 Post St, San Francisco, CA 94102

### Barrett Elementary Schoool

895 Barrett Ave, Morgan Hill, CA 95037

### Stanley Middle School library

3455 School St, Lafayette, CA 94549

### CSU East Bay

25800 Carlos Bee Blvd, Hayward, CA 94542

### American Institute of Mathematics

600 E Brokaw Rd, San Jose, CA 95112

### Nora Suppes Hall 103

224 Panama St, Stanford, CA 94305

### CSU Monterey Bay

**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.

**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.