Unit G5

Geometry through proof.

Geometry has been around since the creation of the earth, and probably even before that. Interestingly the word is derived from the Greek words "geos" (meaning earth) and "metron" ( meaning measure). The subject is, however, very much more than just a measure of objects. It is essentially, a system devised for the study of the properties and relations of constructible figures.

In order to make progress and understand the world in which we live, it is necessary to be very precise about the objects we are dealing with. We want to be certain that a statement will always hold true, not simply because we trust our intuition, but because we can prove it to be true, based on previously established results and a bedrock of fundamental principles. In this way, more elaborate objects can be studied and a greater understanding of their properties can be gained through structured lateral thinking.

Unit G5.1: Review of some fundamental ideas.
Unit G5.2: Straight edge and compass contructions.
Unit G5.3: Establishing results through proof.
Unit G5.4: Pythagoras' Theorem.
Unit G5.5: Investigations with circles.
Unit G5.6: Questions on circles.
Unit G5.7: Obtaining from circles.

Learning Objectives

• In this section the student will be able to
• Construct geometrical figures using compass and straight edge alone
• Fully appreciate a range of geometrical ideas that may have been taken for granted in the past.
• Prove a number of important geometrical theorems.
• Solve geometrical problems involving circles.

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