Straight Lines

Definition: Straight Line

A straight line (or just line) is an [[Bounded Curve|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:

\[ AB \qquad \overline{AB} \qquad BA \qquad \overline{BA} \]

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