More notes

math/computational_geometry/notes.page

@@ -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
 noncrossing diagonals. Maximal means that no more diagonals may be
 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*.