Diagonal (Polygon)
A Line Segment connecting two nonadjacent Vertices of a Polygon. The number ofways a fixed convex 
-gon can be divided into Triangles by nonintersecting diagonals is 
(with 
diagonals), where 
is a Catalan Number. This is Euler's Polygon Division Problem.Counting the number of regions determined by drawing the diagonals of a regular -gon is a more difficult problem, as isdetermining the number of -tuples of Concurrent diagonals (Beeler et al. 1972, Item 2).
The number of regions which the diagonals of a Convex Polygon divide its center if no three are concurrent in itsinterior is
The first few values are 0, 0, 1, 4, 11, 25, 50, 91, 154, 246, ... (Sloane's A006522).See also Catalan Number, Diagonal (Polyhedron), Euler's Polygon Division Problem, Polygon,Vertex (Polygon)
References
Beeler, M.; Gosper, R. W.; and Schroeppel, R. HAKMEM. Cambridge, MA: MIT Artificial Intelligence Laboratory, Memo AIM-239, Feb. 1972. Sloane, N. J. A. SequenceA006522/M3413in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.
- Jacobsthal Number
- Jacobsthal Polynomial
- Jaco-Shalen-Johannson Torus Decomposition
- Janko Groups
- Japanese Triangulation Theorem
- Jarnick's Inequality
- j-Conductor
- Jeep Problem
- Jenkins-Traub Method
- Jensen Polynomial
- Jensen's Formula
- Jensen's Inequality
- Jerabek's Hyperbola
- Jerk
- j-Function
- Jinc Function
- j-Invariant
- Jitter
- Joachimsthal's Equation
- Johnson Circle
- Johnson's Equation
- Johnson Solid
- Johnson's Theorem
- Join (Graph)
- Join (Spaces)