Hexagon

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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

Bild:Sechseck-Zeichnung.png

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:

<math> \ 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:

<math> r_i = \ frac {A} {2} \ sqrt {3} </math>

formula for the surface computation

<math> 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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Nature

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.

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see also

 

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