Enneagon
Encyclopedia
In geometry
, a nonagon icon (or enneagon ˈ) is a nine-sided polygon
.
The name "nonagon" is a prefix
hybrid formation, from Latin
(nonus, "ninth" + gonon), used equivalently, attested already in the 16th century in French nonogone and in English from the 17th century. The name "enneagon" comes from Greek
enneagonon (εννεα, nine + γωνον (from γωνία = corner)), and is arguably more correct, though somewhat less common.
A regular nonagon has internal angle
s of 140°. The area of a regular nonagon of side length a is given by
there are methods of construction that produce very close approximations.
Below is a close approximation of a regular nonagon. The approximate angle error is given in the animation.
is often drawn as a regular nonagon with all 36 edges connected. This graph also represents an orthographic projection
of the 9 vertices and 36 edges of the 8-simplex. Three other rectified
forms also project inside of a regular enneagon:
have a song entitled "Nonagon" on their children's album "Here Come the 123s
." It refers to both an attendee at a party at which "everybody in the party is a many-sided polygon" and a dance they perform at this party.
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, a nonagon icon (or enneagon ˈ) is a nine-sided polygon
Polygon
In geometry a polygon is a flat shape consisting of straight lines that are joined to form a closed chain orcircuit.A polygon is traditionally a plane figure that is bounded by a closed path, composed of a finite sequence of straight line segments...
.
The name "nonagon" is a prefix
Prefix
A prefix is an affix which is placed before the root of a word. Particularly in the study of languages,a prefix is also called a preformative, because it alters the form of the words to which it is affixed.Examples of prefixes:...
hybrid formation, from Latin
Latin
Latin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...
(nonus, "ninth" + gonon), used equivalently, attested already in the 16th century in French nonogone and in English from the 17th century. The name "enneagon" comes from Greek
Greek language
Greek is an independent branch of the Indo-European family of languages. Native to the southern Balkans, it has the longest documented history of any Indo-European language, spanning 34 centuries of written records. Its writing system has been the Greek alphabet for the majority of its history;...
enneagonon (εννεα, nine + γωνον (from γωνία = corner)), and is arguably more correct, though somewhat less common.
A regular nonagon has internal angle
Internal angle
In geometry, an interior angle is an angle formed by two sides of a polygon that share an endpoint. For a simple, convex or concave polygon, this angle will be an angle on the 'inner side' of the polygon...
s of 140°. The area of a regular nonagon of side length a is given by
Construction
Although a regular nonagon is not constructible with compass and straightedgeCompass and straightedge
Compass-and-straightedge or ruler-and-compass construction is the construction of lengths, angles, and other geometric figures using only an idealized ruler and compass....
there are methods of construction that produce very close approximations.
Below is a close approximation of a regular nonagon. The approximate angle error is given in the animation.
Graphs
The K9 complete graphComplete graph
In the mathematical field of graph theory, a complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique edge.-Properties:...
is often drawn as a regular nonagon with all 36 edges connected. This graph also represents an orthographic projection
Orthographic projection
Orthographic projection is a means of representing a three-dimensional object in two dimensions. It is a form of parallel projection, where all the projection lines are orthogonal to the projection plane, resulting in every plane of the scene appearing in affine transformation on the viewing surface...
of the 9 vertices and 36 edges of the 8-simplex. Three other rectified
Rectification (geometry)
In Euclidean geometry, rectification is the process of truncating a polytope by marking the midpoints of all its edges, and cutting off its vertices at those points...
forms also project inside of a regular enneagon:
8-simplex (8D) |
Rectified 8-simplex Rectified 8-simplex In eight-dimensional geometry, a rectified 8-simplex is a convex uniform 8-polytope, being a rectification of the regular 8-simplex.There are unique 3 degrees of rectifications. Vertices of the rectified 8-simplex are located at the edge-centers of the 8-simplex. Vertices of the birectified... (8D) |
Birectified 8-simplex (8D) |
Trirectified 8-simplex (8D) |
Pop culture references
They Might Be GiantsThey Might Be Giants
They Might Be Giants is an American alternative rock band formed in 1982 by John Flansburgh and John Linnell. During TMBG's early years Flansburgh and Linnell were frequently accompanied by a drum machine. In the early 1990s, TMBG became a full band. Currently, the members of TMBG are...
have a song entitled "Nonagon" on their children's album "Here Come the 123s
Here Come the 123s
Here Come the 123s is the 13th studio album by They Might Be Giants. It is the sequel to the group's 2005 album Here Come the ABCs. The songs are edutainment music aimed at kids, this time dealing with numbers. Like ABCs, there is a CD and DVD...
." It refers to both an attendee at a party at which "everybody in the party is a many-sided polygon" and a dance they perform at this party.
External links
- Properties of a Nonagon (with interactive animation)
- Nonagrams