Geometry Homework

Last night my youngest son came and asked me to help him with his geometry homework. As part of the coursework required for my degree in electrical engineering I managed to pick up a minor in mathematics. I also have a minor in physics but that really wasn't important for last night's assignment.

Geometry is one of those topics that you really only experience at one time during your path to greater mathematical understanding. While you may continue to use one or two geometric formulas, the bulk of geometry is so different from all other topics that I was concerned I wouldn't be able to help my son.

He brought down his homework and we looked at it together. There were three proofs. His whole assignment was three problems that took up a single piece of paper. The first two problems had the hard part done. It was left to my son to label each of the steps required to go from "given" to "proof." He had done a fairly good job at guessing the labels. However the third and final problem required him to develop the steps on his own and that really had him confused.

I pulled out a scratch piece of paper and started working out the proof myself. Half a sheet of paper later, I had gone in a circle and was no closer to a solution than a monkey with a dart. So I put down my pencil and thought about the problem. Geometry proofs are like driving a car. You have a starting point and know your ending point. It is then up to you to use a series of theorems and postulates like roads to reach your destination. While it is possible to get in your car and drive around until you find your destination, a lot of gas can be wasted. It is much more efficient to map out a direct path.

I picked up my pencil and noted a couple of things that would take me from the start to the end as quickly as possible. The whole problem took about three steps and I was done. Then I could explain the problem to my son and help him get the answer on his own.

Even though it has been almost 30 years since I had geometry, I was still able to help my son with his homework. It isn't because I have a great memory and can still remember back that far. It is because geometric proofs teach you how to use simple steps to solve larger problems. That is all computer programming is. Since I have been programming for over 20 years, the skills I learned back in high-school have constantly been used and I was able to help my son. I guess I'd better apologize to my old math teacher from when I said, "I'll never use this."