# Dictionary Definition

heptagon n : a seven-sided polygon

# User Contributed Dictionary

## English

### Etymology

Since 16th century, from ἑπτάγωνον (heptagonon), from ἑπτά (hepta), seven, + γωνία (gonia), angle.### Noun

- A polygon with seven sides and seven angles.

#### Translations

A polygon with seven sides and seven angles

#### Related terms

# Extensive Definition

In geometry, a heptagon is a
polygon with seven sides
and seven angles. In a
regular
heptagon, in which all sides and all angles are equal, the sides
meet at an angle of 5π/7 radians, 128.5714286 degrees.
Its Schläfli
symbol is . The area of a regular heptagon of side length a is
given by

- A = \fraca^2 \cot \frac \simeq 3.63391 a^2.

The heptagon is also sometimes referred to as the
septagon, using "sept-" (an elision of septua-,
a Latin-derived
numerical
prefix, rather than hepta-, a
Greek-derived
numerical prefix). The OED
lists "septagon" as meaning "heptagonal".

## Construction

A regular heptagon is not constructible with compass and straightedge but is constructible with a marked ruler and compass. This type of construction is called a Neusis construction. It is also constructible with compass, straightedge and angle trisector. The impossibility of straightedge and compass construction follows from the observation that 2cos(2π/7) ≈ 1.247 is a zero of the irreducible cubic x3 + x2 - 2x - 1. Consequently this polynomial is the minimal polynomial of 2cos(2π/7), whereas the degree of the minimal polynomial for a constructible number must be a power of 2.## Heptagrams

Two kinds of heptagrams can be constructed
from regular heptagons, labeled by Schläfli symbols , and , with
the divisor being the
interval of connection.

## External links

heptagon in Asturian: Heptágonu

heptagon in Azerbaijani: Düzgün
yeddibucaqlı

heptagon in Catalan: Heptàgon

heptagon in Czech: Sedmiúhelník

heptagon in German: Siebeneck

heptagon in Spanish: Heptágono

heptagon in French: Heptagone

heptagon in Galician: Heptágono

heptagon in Korean: 칠각형

heptagon in Italian: Ettagono

heptagon in Georgian: ჰეპტაგონი

heptagon in Hungarian: Hétszög

heptagon in Dutch: Zevenhoek

heptagon in Japanese: 七角形

heptagon in Norwegian: Heptagon

heptagon in Polish: Siedmiokąt foremny

heptagon in Portuguese: Heptágono

heptagon in Russian: Правильный
семиугольник

heptagon in Serbian: Седмоугао

heptagon in Finnish: Seitsenkulmio

heptagon in Swedish: Heptagon

heptagon in Thai: รูปเจ็ดเหลี่ยม

heptagon in Chinese: 七边形