Heptagon
From Free net encyclopedia
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 approximately 128.6 degrees. Its Schläfli symbol is {7}. The area of a regular heptagon of side length a is given by
- <math>A = \frac{7}{4}a^2 \cot \frac{\pi}{7} \simeq 3.63391 a^2.</math>
A regular heptagon is not constructible with compass and straightedge but is constructible with a marked ruler and compass.
The United Kingdom currently (2003) has two heptagonal coins, the 50p and 20p pieces. The 20 eurocent coin has cavities placed similarly. Strictly, the shape of the coins is a curvilinear heptagon: the sides are curved outwards so that the coin will roll smoothly in vending machines.
The heptagon is also sometimes referred to as the septagon, using "sept-" (an elision of septua-, a Latin-derived numerical prefix) for seven, rather than hepta-, a Greek-derived numerical prefix.
See also
de:Siebeneck es:Heptágono fr:Heptagone pt:Heptágono sv:Heptagon