# Hexagon

## to meaning

a hexagon or also a Hexagon (of Greek hexadecimal six) a Polygon ( polygon) is consisting of six corners and six sides.

## mathematical connections

one often means a regular hexagon with hexagon. This can be designed very simply from a circle, by one the radius of the circle six times upthe edge of circle clears away. The received points are the corners of a regular hexagon. For the first time Euklid in its 15 described the underlying connections. mathematical set 4. Book the elements. The contained triangles are equilateral triangles

the sum of the angles of a regular hexagon amount to 720° andresults from the formula. Whereby the Variabele n=6 is because Hexagon 6 sides has:

[itex] \ sum {\ alpha =} (n - 2) \ cdot 180^ \ circ = 4 \ cdot 180^ \ circ = 720^ \ circ< /math>

The angle in the regular hexagon amounts to

< math> \ alpha = \ frac {(n - 2)}{n} \ cdot 180^ \ circ = \ frac {2} {3}\ 180^ cdot \ circ = 120^ \ circ< /math>

The mathematical relations between the radius of the Umkreises, the length of a side of the regular hexagon and the surface describes the following formulas:

[itex] r_i = \ frac {A} {2} \ sqrt {3} [/itex]

### formula for the surface computation

[itex] A = \ frac {3} {2} a^2\ {3} /math <sqrt>

With regular hexagons one can completely fill one level. A such filling is called hexagonal structure. This arrangement steps frequently also in nature on (see “occurrences of hexagons and hexagonal structures”).

## occurrences of hexagons and hexagonal structures

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### art, culture, geography & politics

• architecture: in many cultures the Hexagon was a fundamental element for the organization of windows, tiles and mosaics. Examples are Fresken at the cathedral to Pisa or wall elements of some buildingsin Pompeji; likewise the Glastonbury Abbey is within (meant) a Hexagons
• M. C. E: many of its mosaic variations are based on hexagons
• David star: one connects alternating corner points of a hexagon keeps one a hexadecimal gram, also for David star mentioned, the symbol of the Israeli state State of
• France: Due to its form the territory of France lain on the European mainland is called also l'hexagone. See also (down): coincidental form agreement.
• with the Colombian Desana Indians the hexagon had fundamental mythologische meaning and outlined also their territory, whereby the six corners in each case by one Wasserfall marked were
• with many strategy plays particularly with Cosims so mentioned (conflict simulation plays) consists the playing field of a hexagon raster on a map. Thus there are more directions of motion than with a square structural grid (e.g. Chessboard).

### coincidental form agreement

• winter hexagon: a star picture of which an irregular hexagonnational form
• forms: the Hexagon is the national symbol of France, because the national form is in approximately hexagonal. For this reason the French 1 is - and to 2-Euro-Münzen a representative tree in a Hexagon on the back, and the marshal of France carries its seven starson the shoulder pieces in the hexagon arranged.