More notes

master
Levi Pearson 2014-01-25 00:25:39 -07:00
parent 84af95d818
commit ec9c2eb3a2
1 changed files with 27 additions and 0 deletions

View File

@ -45,3 +45,30 @@ $P$, not touching $\partial P$ except at endpoints. Two diagonals are
: A decomposition of $P$ into triangles by a maximal set of : A decomposition of $P$ into triangles by a maximal set of
noncrossing diagonals. Maximal means that no more diagonals may be noncrossing diagonals. Maximal means that no more diagonals may be
added without crossing. added without crossing.
**Lemma 1.3**
: Every polygon with more than three vertices has a diagonal.
**Theorem 1.4**
: Every polygon has a triangulation.
*polyhedron*
: A 3-d generalization of a polygon, a solid bounded by finitely many
polygons.
*tetrahedron*
: A pyramid with a triangular base. The simplest polyhedron.
Polygon triangularization generalizes to polyhedron
*tetrahedralization*, which is partitioning of the interior into
tetrahedrons whose edges are diagonals of the polyhedron. Not all
polyhedrons can be tetrahedralized!
**Theorem 1.8**
: Every triangularization of a polygon $P$ with $n$ vertices has $n -
2$ triangles and $n - 3$ diagonals.
*ear*
: Three consecutive vertices $a, b, c$ form an *ear* of a polygon if
$a c$ is a diagonal of the polygon. The vertex $b$ is called the ear
*tip*.