All Topics  
Heptagon

 

 
   Email Print
   Bookmark   Link
 

 

Heptagon
 
 
  Topics Heptagon Topic Home

In geometry
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 heptagon is a polygon
Polygon

In geometry a polygon is traditionally a plane Shape that is bounded by a closed curve path or circuit, composed of a finite sequence of straight line segments ....
 with seven sides and seven angle
Angle

In geometry and trigonometry, an angle is the figure formed by two Ray sharing a common endpoint, called the vertex of the angle . The magnitude of the angle is the "amount of rotation" that separates the two rays, and can be measured by considering the length of circular arc swept out when one ray is rotated about the vertex to coincide...
s. In a regular
Regular polygon

A regular polygon is a polygon which is Equiangular polygon and equilateral . Regular polygons may be convex or Star polygon....
 heptagon, in which all sides and all angles are equal, the sides meet at an angle of 5p/7 radian
Radian

The radian is a unit of plane angle, equal to 180/pi Degree , or about 57.2958 degrees, or about 57?17'45?. It is the standard unit of angular measurement in all areas of mathematics beyond the elementary level....
s, 128.5714286 degree
Degree (angle)

A degree , usually denoted by ? , is a measurement of plane angle, representing 1/360 of a Turn ; one degree is equivalent to p/180 radians....
s. Its Schläfli symbol
Schläfli symbol

In mathematics, the Schl?fli symbol is a notation of the form that defines regular polytopes and tessellations.The Schl?fli symbol is named after the 19th-century mathematician Ludwig Schl?fli who made important contributions in geometry and other areas....
 is . The area of a regular heptagon of side length a is given by

The heptagon is also sometimes referred to as the septagon, using "sept-" (an elision of septua-, a Latin
Latin

Latin is an Italic language, historically spoken in Latium and Ancient Rome. Through the Military history of the Roman Empire, Latin spread throughout the Mediterranean and a large part of Europe....
-derived numerical prefix
Numerical prefix

Numerical prefixes are usually derived from the words for numbers in various languages, most commonly Greek language and Latin, although this is not always the case....
, rather than hepta-, a Greek
Greek language

Greek is an Indo-European languages native to the southern Balkan peninsula, the language of the Greek people. It forms an independent branch within Indo-European....
-derived numerical prefix).






Discussion
Ask a question about 'Heptagon'
Start a new discussion about 'Heptagon'
Answer questions from other users
Full Discussion Forum



Encyclopedia


In geometry
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 heptagon is a polygon
Polygon

In geometry a polygon is traditionally a plane Shape that is bounded by a closed curve path or circuit, composed of a finite sequence of straight line segments ....
 with seven sides and seven angle
Angle

In geometry and trigonometry, an angle is the figure formed by two Ray sharing a common endpoint, called the vertex of the angle . The magnitude of the angle is the "amount of rotation" that separates the two rays, and can be measured by considering the length of circular arc swept out when one ray is rotated about the vertex to coincide...
s. In a regular
Regular polygon

A regular polygon is a polygon which is Equiangular polygon and equilateral . Regular polygons may be convex or Star polygon....
 heptagon, in which all sides and all angles are equal, the sides meet at an angle of 5p/7 radian
Radian

The radian is a unit of plane angle, equal to 180/pi Degree , or about 57.2958 degrees, or about 57?17'45?. It is the standard unit of angular measurement in all areas of mathematics beyond the elementary level....
s, 128.5714286 degree
Degree (angle)

A degree , usually denoted by ? , is a measurement of plane angle, representing 1/360 of a Turn ; one degree is equivalent to p/180 radians....
s. Its Schläfli symbol
Schläfli symbol

In mathematics, the Schl?fli symbol is a notation of the form that defines regular polytopes and tessellations.The Schl?fli symbol is named after the 19th-century mathematician Ludwig Schl?fli who made important contributions in geometry and other areas....
 is . The area of a regular heptagon of side length a is given by

The heptagon is also sometimes referred to as the septagon, using "sept-" (an elision of septua-, a Latin
Latin

Latin is an Italic language, historically spoken in Latium and Ancient Rome. Through the Military history of the Roman Empire, Latin spread throughout the Mediterranean and a large part of Europe....
-derived numerical prefix
Numerical prefix

Numerical prefixes are usually derived from the words for numbers in various languages, most commonly Greek language and Latin, although this is not always the case....
, rather than hepta-, a Greek
Greek language

Greek is an Indo-European languages native to the southern Balkan peninsula, the language of the Greek people. It forms an independent branch within Indo-European....
-derived numerical prefix). The OED
Oxford English Dictionary

The Oxford English Dictionary , published by the Oxford University Press , is a comprehensive dictionary of the English language. Two fully-bound print editions of the OED have been published under its current name, in 1928 and 1989; as of December 2008 the dictionary's current editors have completed a quarter of the third edition....
 lists "septagon" as meaning "heptagonal".

Construction

A regular heptagon is not constructible
Constructible polygon

In mathematics, a constructible polygon is a regular polygon that can be Compass and straightedge constructions. 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 or angles using only an Idealization ruler and Compass ....
 but is constructible with a marked ruler
Ruler

A ruler, or rule, is an Measuring instrument used in geometry, technical drawing and engineering/building to measure distances and/or to rule straight lines....
 and compass. This type of construction is called a Neusis construction
Neusis construction

The neusis is a geometric construction method that was used in antiquity by Greek mathematicians....
. It is also constructible with compass, straightedge and angle trisector. The impossibility of straightedge and compass construction follows from the observation that 2cos(2p/7) ˜ 1.247 is a zero of the irreducible
Irreducible polynomial

In mathematics, the adjective irreducible means that an object cannot be expressed as a product of at least two non-trivial factors in a given set....
 cubic
Cubic function

In mathematics, a cubic function is a function of the formwhere a is nonzero; or in other words, a polynomial of Degree of a polynomial three....
 x3 + x2 - 2x - 1. Consequently this polynomial is the minimal polynomial of 2cos(2p/7), whereas the degree of the minimal polynomial for a constructible number
Constructible number

A point in the Euclidean plane is a constructible point if, given a fixed coordinate system , the point can be constructed with Compass and straightedge constructions....
 must be a power of 2.
Neusis Heptagon

Approximation

A decent approximation for practical use with an accuracy of is shown in the drawing. Let lie on the circumference of the circumcircle. Draw arc . Then gives an approximation for the edge of the heptagon.

Heptagrams


Two kinds of heptagram
Heptagram

A heptagram or septegram is a seven-pointed Star drawn with seven straight strokes....
s can be constructed from regular heptagons, labeled by Schläfli symbols , and , with the divisor
Divisor

In mathematics, a divisor of an integer n, also called a factor of n, is an integer which evenly divides n without leaving a remainder....
 being the interval of connection.

Heptagrams

Blue, and green heptagrams inside a red heptagon.

Uses

The United Kingdom
United Kingdom

The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom , the UK or Britain,is a sovereign state located off the northwestern coast of continental Europe....
 currently (2008) has two heptagonal coin
Coin

A coin is a piece of hard material, usually metal or a metallic material, usually in the shape of a Disk , and most often issued by a government....
s, the 50p and 20p pieces, and the Barbados
Barbados

Barbados , situated just east of the Caribbean Sea, is an independent Continental Island-island nation in the western Atlantic Ocean. Located at roughly 13? North of the equator and 59? West of the prime meridian, it is considered a part of the Lesser Antilles....
 Dollar is also heptagonal. The 20 eurocent coin has cavities placed similarly. Strictly, the shape of the coins is a curvilinear heptagon to make them curves of constant width
Curve of constant width

In geometry, a curve of constant width is a Convex set planar shape whose width, measured by the distance between two opposite parallellines touching its boundary, is the same regardless of the direction of those two parallel lines....
: the sides are curved outwards so that the coin will roll smoothly in vending machine
Vending machine

A vending machine provides various snacks, beverages, and other products to consumers. The idea is to vend products without a cashier. Items sold via vending machines vary by country and region....
s. The Brazil
Brazil

Brazil , officially the Federative Republic of Brazil , is a country in South America. It is the List of countries and outlying territories by total area country by geographical area, occupying nearly half of South America, the List of countries by population country, and the fourth most populous democracy in the world....
ian 25 cents coin has a heptagon inscribed in the coin's disk.

Some old versions of Coat of arms of Georgia (country)
Coat of arms of Georgia (country)

Georgia 's coat of arms was adopted on 1st October 2004. It is partially based on the medieval arms of the Georgian royal house of Bagrationi....
 including Soviet days had used heptagram as an element.

See also

  • Heptagram
    Heptagram

    A heptagram or septegram is a seven-pointed Star drawn with seven straight strokes....
  • Heptagonal tiling
    Order-3 heptagonal tiling

    In geometry, the order-3 heptagonal tiling is a regular tiling of the hyperbolic plane. It has Schl?fli symbol of .The image shows a Poincar? disk model projection of the hyperbolic plane....


External links

With interactive animation