Hendecagon
Encyclopedia
In geometry
, a hendecagon (also undecagon) is an 11-sided polygon
. (The name hendecagon, from Greek hendeka 'eleven' and gon– 'corner', is often preferred to the hybrid undecagon, whose first syllable un– is Latin for 'one'.)
s of 147.27 degree
s.
The area of a regular hendecagon with side length a is given by
A regular hendecagon is not constructible
with compass and straightedge
.
coin, the loonie
, is similar to, but not exactly, a regular hendecagonal prism
, as is the Indian two-rupee coin.
It was also patterned on the Susan B. Anthony dollar
of the United States from 1979–1981 and again in 1999 and Sri Lanka 10 Rupees 2009.
using compass and straightedge
. Because 11 is not a Pierpont prime
, construction of a regular hendecagon is still impossible even with the usage of an angle trisector
.
for 10-dimensional uniform polytopes of the simplex family, projected in a skew orthogonal projection.
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 hendecagon (also undecagon) is an 11-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 hendecagon, from Greek hendeka 'eleven' and gon– 'corner', is often preferred to the hybrid undecagon, whose first syllable un– is Latin for 'one'.)
Regular hendecagon
A regular hendecagon has internal angleInternal 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 147.27 degree
Degree (angle)
A degree , usually denoted by ° , is a measurement of plane angle, representing 1⁄360 of a full rotation; one degree is equivalent to π/180 radians...
s.
The area of a regular hendecagon with side length a is given by
A regular hendecagon is not constructible
Constructible polygon
In mathematics, a constructible polygon is a regular polygon that can be constructed with compass and straightedge. For example, a regular pentagon is constructible with compass and straightedge while a regular heptagon is not....
with compass and straightedge
Compass 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....
.
Use in coinage
The Canadian dollarCanadian dollar
The Canadian dollar is the currency of Canada. As of 2007, the Canadian dollar is the 7th most traded currency in the world. It is abbreviated with the dollar sign $, or C$ to distinguish it from other dollar-denominated currencies...
coin, the loonie
Loonie
The Canadian 1 dollar coin is a gold-coloured, bronze-plated, one-dollar coin introduced in 1987. It bears images of a common loon, a bird which is common and well known in Canada, on the reverse, and of Queen Elizabeth II on the obverse.The design for the coin was meant to be a voyageur theme,...
, is similar to, but not exactly, a regular hendecagonal prism
Hendecagonal prism
In geometry, the hendecagonal prism is one in an infinite set of convex prisms formed by square sides and two regular polygon caps, in this case two hendecagons....
, as is the Indian two-rupee coin.
It was also patterned on the Susan B. Anthony dollar
Susan B. Anthony dollar
The Susan B. Anthony dollar is a United States coin minted from 1979 to 1981, and again in 1999. It depicts women's suffrage campaigner Susan B. Anthony on a dollar coin. It was the first circulating U.S. coin with the portrait of an actual woman rather than an allegorical female figure such as...
of the United States from 1979–1981 and again in 1999 and Sri Lanka 10 Rupees 2009.
Hendecagrams
The hendecagon is the perimeter of four regular hendecagrams, {11/2}, {11/3}, {11/4}, {11/5}.Construction
A regular hendecagon cannot be constructedConstructible polygon
In mathematics, a constructible polygon is a regular polygon that can be constructed with compass and straightedge. For example, a regular pentagon is constructible with compass and straightedge while a regular heptagon is not....
using compass and straightedge
Compass 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....
. Because 11 is not a Pierpont prime
Pierpont prime
A Pierpont prime is a prime number of the form2^u 3^v + 1\,for some nonnegative integers u and v. They are named after the mathematician James Pierpont....
, construction of a regular hendecagon is still impossible even with the usage of an angle trisector
Neusis construction
The neusis is a geometric construction method that was used in antiquity by Greek mathematicians.- Geometric construction :The neusis construction consists of fitting a line element of given length in between two given lines , in such a way that the line element, or its...
.
Petrie polygons
The regular hendecagon is the Petrie polygonPetrie polygon
In geometry, a Petrie polygon for a regular polytope of n dimensions is a skew polygon such that every consecutive sides belong to one of the facets...
for 10-dimensional uniform polytopes of the simplex family, projected in a skew orthogonal projection.
10-simplex 10-simplex In geometry, a 10-simplex is a self-dual regular 10-polytope. It has 11 vertices, 55 edges, 165 triangle faces, 330 tetrahedral cells, 462 5-cell 4-faces, 462 5-simplex 5-faces, 330 6-simplex 6-faces, 165 7-simplex 7-faces, 55 8-simplex 8-faces, and 11 9-simplex 9-faces... |
Rectified 10-simplex Rectified 10-simplex In ten-dimensional geometry, a rectified 10-simplex is a convex uniform 10-polytope, being a rectification of the regular 10-simplex.These polytopes are part of a family of 527 uniform 10-polytopes with A10 symmetry.... |
Birectified 10-simplex |
Trirectified 10-simplex |
Quadrirectified 10-simplex |
External links
- Properties of an Undecagon (hendecagon) With interactive animation