Math Resource Page

Working on the exercises in class, we have mentioned some conjectures about lines and planes in space. In some cases I have told you they are true. For example in Chapter 1, Exercise 12, we discussed conjectures about parallel lines in $\R^3$ and their projections to the picture plane. In constructing the block letter T, the fourth construction (using proportions) required a fact we had not proved.

This page collects together some of these facts and definitions so that you can see statements of the theorems. Each theorem comes with a proof, if you care to read it. You are not expected to know all these proofs. However we will be working on how to prove things, and these could provide helfpul examples. You are allowed to rely on these facts, which is why we occasionally go over them and record an official correct answer. The ones chosen here are ones I have relied on in some of the justifications for constructions such as completing the T.

Definitions for lines and planes in 3-dimensional space: the terms "co-planar" and "parallel"

Some axioms for 3-D goemetry

Statements and proofs of some things we have used so far

Vocabulary: images versus projections

Definitions and notation for E^3: a slightly different but equivalent version to what is in the textbook.

Solutions to homework problems E5.2 and E5.3

Notations and facts concerning projections