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	{{otheruses}}
			==Hexagon construction==
	{\| border="1" bgcolor="#ffffff" cellpadding="5" align="right" style="margin-left:10px" width="250"
		⚫	A regular hexagon is ] with ]. The following is a step-by-step animated method of this, given by ]'s '']'', Book IV, Proposition 15.
	!bgcolor=#e7dcc3 colspan=2\|Regular hexagon
			]
	\|-
	\|align=center colspan=2\|]<BR>A regular hexagon, {6}
	\|-
	\|bgcolor=#e7dcc3\|]s and ]\|\|6
	\|-
	\|bgcolor=#e7dcc3\|]s\|\|{6}<BR>t{3}
	\|-
	\|bgcolor=#e7dcc3\|]s\|\|]]]<BR>]]]
	\|-
	\|bgcolor=#e7dcc3\|]\|\|] (D<sub>6</sub>)
	\|-
	\|bgcolor=#e7dcc3\|]<BR>(with ''t''=edge length)\|\|<math>A = \frac{3 \sqrt{3}}{2}t^2</math><BR><math> \simeq 2.598076211 t^2.</math>
	\|-
	\|bgcolor=#e7dcc3\|]<BR>(]s)\|\|120°
	\|}

			==Hexagon by man and nature==
	In ], a '''hexagon''' is a ] with six edges and six ]. A regular hexagon has ] {6}.

	== Regular hexagon ==
⚫	~~] with ]. The following is a step-by-step animated method of this, given by ]'s '']'', Book IV, Proposition 15.]]~~

	The internal ]s of a regular hexagon (one where all sides and all angles are equal) are all
	120] and the hexagon has 720 degrees. It has 6 lines of symmetry. Like ]s and ] ]s, regular hexagons fit together without any gaps to ''tile the plane'' (three hexagons meeting at every vertex), and so are useful for constructing ]s.
	The cells of a ] ] are hexagonal for this reason and because the shape makes efficient use of space and building materials. The ] of a regular triangular lattice is the honeycomb tessellation of hexagons.

	The area of a regular hexagon of side length <math>t\,\!</math> is given by
	<math>A = \frac{3 \sqrt{3}}{2}t^2 \simeq 2.598076211 t^2.</math>

	The perimeter of a regular hexagon of side length <math>t\,\!</math> is, of course, <math>6t\,\!</math>, its maximal diameter <math>2t\,\!</math>, and its minimal diameter <math>t\sqrt{3}\,\!</math>.

	There is no ] made of regular hexagons. The ]s with some hexagonal faces are the ], ], ] (of ] ball and ] fame), ] and the ].

	==Hexagons: in nature and by humankind==

	<gallery>		<gallery>
			Image:Fort-Jefferson Dry-Tortugas.jpg\|
	Image:Honey_comb.jpg\|A beehive ]
	Image:Carapax.svg\|The scutes of a turtle's ]
	Image:Saturn_hexagonal_north_pole_feature.jpg\|North polar hexagonal cloud feature on ], discovered by ] and confirmed in 2006 by ]
	Image:Snowflake 300um LTSEM, 13368.jpg\|Micrograph of a snowflake
	Image:Hexa-peri-hexabenzocoronene ChemEurJ 2000 1834.jpg\|Crystal structure of a ] composed of hexagonal aromatic rings reported by Müllen and coworkers in Chem. Eur. J., 2000, 1834-1839.
	Image:Giants causeway closeup.jpg\|Naturally formed ] columns from ] in ]; large masses must cool slowly to form a polygonal fracture pattern
	Image:Fort-Jefferson Dry-Tortugas.jpg\|An aerial view of Fort Jefferson in ]
	Image:Jwst front view.jpg\|The ] mirror is composed of 18 hexagonal segments.
	Image:France.jpg\| ] has a vaguely hexagonal shape. In French, "L'hexagone" sometimes refers to the country.
	</gallery>		</gallery>

⚫	== See also ==
	*]: 6-sided star within a regular hexagon
	*]: single path, 6-sided star, within a hexagon
	*]: a ] of hexagons in a plane
⚫	*]

	== External links ==		== External links ==
	* {{MathWorld\|title=Hexagon\|urlname=Hexagon}}
	* With interactive animation		* With interactive animation

	*
		⚫	==See also==
	*
		⚫	*]
	*
	* - from ] (27 March 2007)

	{{Polygons}}		{{Polygons}}

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Revision as of 03:28, 17 January 2008

fuck fuck fuck shit

Hexagon construction

A regular hexagon is constructible with compass and straightedge. The following is a step-by-step animated method of this, given by Euclid's Elements, Book IV, Proposition 15.

Hexagon by man and nature

External links

Definition and properties of a hexagon With interactive animation

Revision as of 03:28, 17 January 2008

Hexagon construction

Hexagon by man and nature

External links

See also