Some Games Helpful in Teaching Geometric Concepts

Series Summary

Most students dread any type of mathematics. Algebra, geometry, trigonometry and calculus are four words that can make any student's palms sweat. Understanding the difference between each subject can be of great help in the learning process. Geometry deals with size, shape and space properties. Trigonometry deals mostly with plane triangles and the relationships between the angles and sides of a triangle. In this free video series, learn about geometry and trigonometry from two assistant mathematics professors. First, learn some games that help in the process of learn geometry, basic geometrical concepts for students, step-by-step geometrical proofs and how to simplify geometrical proofs. Next, they talk about converting degrees to radians, using a calculator for trigonometry and how to use trigonometry. Finally, learn what careers these subjects are beneficial to.

Video Transcript

"Hi, we're going to talk about how to play some simple geometry games, and the first game we're going to play is called hex. One of the inventors was John Nash, and it's a very simple game played on a board made up of hexagonal cells. Game play consists of placement of stones, or you can use a marker and make X's. Black goes first. Any cell at all is open for play, and white goes second, and this continues. The goal is to build a bridge across the board, which I'll show you now. Here, for instance, is a win for purple. The purple X's make a complete chain, path that, of touching hexagonal cells from one edge of the board to the opposite. A strategy in two player hex can be either fairly simple or complicated. The simplest strategy is exhibited here. If the green player can get this position, we call them bridges, then it's going to be a win, no matter whether where the second player places his piece. The idea is that the shaded cells have to be open, and now a complete path can be made. It's impossible to block it. The next game is a sort of generalized tic-tac-toe. This is a giant tic-tac-toe board; a lot more squares than the usual size, but we're going to play in the same way as in normal tic-tac-toe. Going to take turns putting our X's and O's. You can play this when with the goal of getting three in a row, just like in tic-tac-toe, but much more interesting is to try and shoot for this shape. It consists of four in a row, and two more in a row offset, but all of them touching along the side of the square. The shape has been named snaky, so this sort of tic-tac-toe could be called snaky tic-tac-toe. Games like these are quite useful for practicing the art of coming up with a strategy. That's something that you're also going to need whenever you write down a geometry proof. You'll need to think ahead, and decide which step to take in order to reach your goal."