# Introduction to Geometry - Art of Problem Solving

(3 credits)*Prerequisites:* or permission of instructor. Logic and problem solving will be used to discover geometric concepts. Examples from theorems of great mathematicians of the past will be studied. Students will be expected to understand and construct logical arguments. Use of technology to explore geometric relationships will be an integral part of the course.

## Geometry - Art of Problem Solving

Photo provided by Flickr

### Problem Solving in Geometry | Johns Hopkins Center for Talented Youth

Our novel methodology uses (i) deductive reasoning to generate a partial program from logical constraints, (ii) numerical methods to evaluate the partial program, thus creating geometric models which are solutions to the original problem, and (iii) inductive synthesis to read off new constraints that are then applied to one more round of deductive reasoning leading to the desired deterministic program. By the combination of methods we were able to solve problems that each of the methods was not able to solve by itself.

### Algebra: Word Problems: Solving Geometry Problem (1) - YouTube

We describe a framework that combines deductive, numeric, and inductive reasoning to solve geometric problems. Applications include the generation of geometric models and animations, as well as problem solving in the context of intelligent tutoring systems.

Photo provided by Flickr