Introduction to Geometric Construction

In Geometry, the term construction refers to a precise way of drawing using two tools, an unmarked straightedge and a compass. The straightedge is assumed to have an infinite length and has no markings.  In constructions, these tools and only these tools must be used to construct lines, curves, and polygons.  Shown below is an animation showing  how to construct a square using compass and straightedge.

Square construction

The Construction Rules

In construction, aside from the tools, there are specific rules to be followed. These rules are the following.  » Read more

Chess and the Axiomatic Systems

Before playing any game, we must follow certain rules.  In a basketball game, certain ways of holding or blocking opponent players call for a foul, while in boxing, the opposing players must at least be on the same weight class during the weigh-in the day before the fight.

For mathematical discussion, let us examine the rules in playing chess. These are the basic rules in chess, they are not complete, but we will use them for the sake of discussion: » Read more