This preview shows pages 1–3. Sign up to view the full content.
Polygon
From Wikipedia, the free encyclopedia
In geometry a
polygon
(pronounced
/ˈpɒlɨɡɒn/
or
/ˈpɒliːɡɒn/
) is traditionally a plane figure that is
bounded by a closed path or
circuit
, composed of a finite sequence of straight line segments (i.e., by a
closed polygonal chain). These segments are called its
edges
or
sides
, and the points where two edges
meet are the polygon's
vertices
or
corners
. The interior of the polygon is sometimes called its
body
. A
polygon is a 2dimensional example of the more general polytope in any number of dimensions.
The word "polygon" derives from the Greek
πολύς
("many") and
γωνία
(g
ō
nia), meaning "knee" or
"angle". Today a polygon is more usually understood in terms of sides.
Usually two edges meeting at a corner are required to form an angle that is not straight (180°);
otherwise, the line segments will be considered parts of a single edge.
The basic geometrical notion has been adapted in various ways to suit particular purposes. For example
in the computer graphics (image generation) field, the term
polygon
has taken on a slightly altered
meaning, more related to the way the shape is stored and manipulated within the computer.
Classification
Contents
1 Classification
1.1 Number of sides
1.2 Convexity
1.3 Symmetry
1.4 Miscellaneous
2 Properties
2.1 Angles
2.2 Area and centroid
2.2.1 Self
intersecting
polygons
2.3 Degrees of freedom
3 Generalizations of
polygons
4 Naming polygons
5 History
6 Polygons in nature
7 Uses for polygons
7.1 Polygons in
computer graphics
8 Pop culture references
9 External links
10 See also
11 References
An assortment of polygons
Page 1 of 11
Polygon  Wikipedia, the free encyclopedia
3/3/2009
http://en.wikipedia.org/wiki/Polygon
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentNumber of sides
Polygons are primarily classified by the number of sides, see naming polygons below.
Convexity
Polygons may be characterised by their degree of convexity:
Convex
: any line drawn through the polygon (and not tangent to an edge or corner) meets its
boundary exactly twice.
Nonconvex
: a line may be found which meets its boundary more than twice.
Simple
: the boundary of the polygon does not cross itself. All convex polygons are simple.
Concave
: Nonconvex and simple.
Starshaped
: the whole interior is visible from a single point, without crossing any edge. The
polygon must be simple, and may be convex or concave.
Selfintersecting
: the boundary of the polygon crosses itself. Branko Grünbaum calls these
coptic
, though this term does not seem to be widely used. The term
complex
is sometimes used in
contrast to
simple
, but this risks confusion with the idea of a
complex polygon
as one which exists
in the complex Hilbert plane consisting of two complex dimensions.
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '09
 CARR

Click to edit the document details