Chapter 5 Geometry

Section 5.1 Elements of Plane Geometry

5.1.1 Introduction

Looking at the stars on a clear, moonless night conveys a vivid impression of the elementary objects of geometry, namely the points. Since time immemorial, people mentally connected the points of light in the night sky by lines which they interpreted as the contours of highly diverse characters. Every building, with its vertex corners, edges, and faces, provides evidence of the practical use of this "heavenly" geometry, ....
On the other hand, the invention of pencils, wax tablets, papyrus or paper enabled people to capture their thoughts and observations "on paper" and to show them to others. For example, the desire to realise a drawing as a physical building resulted in the concept of a plan. A plan is a drawing of an idealised image showing, for example, how a stadium shall look from above.
For the construction of a stadium, significant points are staked out in the terrain. The current status of the project is shown in the following drawing containing the contours and significant points from a plan.

(Measurement) points and lines from a construction plan of a stadium

The drawing can be considered as an idealised image of reality. Along these lines, we will first recapitulate some basic concepts of geometry. Then, applying these concepts, we will construct more complicated figures and geometric solids.