convex polygon - Article Index

Encyclopedia - Catalan Number: Encyclopedia - Catalan Number
In combinatorial mathematics, the Catalan numbers form a sequence of natural numbers that occur in various counting problems; which often...   » Read the article

Encyclopedia - List Of Geometric Shapes: Encyclopedia Ii - List Of Geometric Shapes - Curved
List of geometric shapes - Not composed of circular arcs. Archimedean spiral astroid, paracycle, cubocycloid deltoid ellipse smoothed ...   » Read the article

Encyclopedia - Diagonal: Encyclopedia Ii - Diagonal - Geometry
By analogy, the subset of the Cartesian product X×X of any set X with itself, consisting of all pairs (x,x), is called the diagonal. It ...   » Read the article

Encyclopedia - Polygon Triangulation: Encyclopedia Ii - Polygon Triangulation - Using Monotone Polygons
A monotone polygon is one with a boundary that consists of two parts, each of which consists of points that have incrementing coordinates...   » Read the article

Encyclopedia - Catalan Number: Encyclopedia Ii - Catalan Number - Proof Of The Formula
There are several ways of explaining why the formula given for Cn is correct; that is, why it solves the combinatorial problems listed ab...   » Read the article

Encyclopedia - Polygon Triangulation: Encyclopedia Ii - Polygon Triangulation - Substracting Ears Method
One way to triangulate a simple polygon is by using the assertion that any simple polygon without holes has at least two so called 'ears'...   » Read the article

Encyclopedia - Diagonal: Encyclopedia Ii - Diagonal - Polygons
As applied to a polygon, a diagonal is a line segment joining two vertices that are not adjacent. Therefore a quadrilateral has two diago...   » Read the article

Encyclopedia - Catalan Number: Encyclopedia Ii - Catalan Number - Properties Of The Catalan Numbers
One can verify that an alternative expression for Cn is This shows that Cn is a natural number, which is not a priori obvious from the...   » Read the article