Plane Geometry, An Introduction

Introduction

In approximately 300 B.C., Euclid (biography) laid the foundations for plane geometry in his book The Elements.  He also laid the foundations for number theory, and perhaps mathematics itself.  It is difficult to know how much of this work was his creation - much of it was a careful compilation of earlier results.  The accomplishment is impressive nonetheless.

Euclidean geometry is also known as flat geometry.  This does not mean everything is flat; it means that space consists of straight lines.  In the 19th century, alternate forms of geometry were developed, where lines are not straight.  The earth, for instance, with its lines of latitude and logitude, follows the rules of spherical geometry.  Parallel lines, such as 10 west longitude and 20 west longitude, do indeed meet at a point, namely the north pole, whereas parallel lines on a piece of paper never meet.  For now, let's stick with euclidean geometry. two flavors of geometry

Subsequent theorems are not defined or proved rigorously, but you can prove them analytically if you like; it's not hard.  Embed the geometric figures in the xy plane and derive equations for them.  Then manipulate the equations using algebraic techniques.  But you wouldn't be here if you were interested in an algebraic approach, so let's proceed with "intuitive" geometry.