Straight Lines

Definition: Straight Line

A straight line (or just line) is an unbounded curve whose curvature is zero everywhere.

NOTATION

Straight lines are usually denoted with lowercase Latin letters: $a,b,c,p,q,m,n,l,$ etc.

If we know two points $A$ and $B$ which lie on the line, then we can also denote the line as either of the following:

$$AB\overline{AB}BA\overline{BA}$$

Theorem: Straight Line through Two Points

If $P_1$ and $P_2$ are two distinct points in $n$-dimensional Euclidean space, then there exists one and only one straight line $l$ which contains both points, i.e. $P_1\in l$ and $P_2\in l$.

PROOF

TODO