PlanetMath: hexagon

(more info)

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hexagon

(Definition)

An hexagon is a -sided polygon. The most commonly quoted hexagon is a regular hexagon, having congruent sides and congruent interior angles. Below is an example of a regular hexagon:

$\begin{pspicture}(0,0)(6,5.2) \pspolygon(0,2.598)(1.5,0)(4.5,0)(6,2.598)(4.5,5.1... ...6) \psdots(0,2.598)(1.5,0)(4.5,0)(6,2.598)(4.5,5.196)(1.5,5.196) \end{pspicture}$

Below are some properties of regular hexagons in Euclidean geometry:

The measure of any interior angle of a regular hexagon is $120^{\circ}$ .
The smallest for which a regular -gon has diagonals which are not congruent is . For example, in the regular hexagon below, the diagonal drawn in blue and the one drawn in red are not congruent.

$\begin{pspicture}(0,0)(6,5.2) \psline[linecolor=blue](1.5,0)(1.5,5.196) \psline[... ...6) \psdots(0,2.598)(1.5,0)(4.5,0)(6,2.598)(4.5,5.196)(1.5,5.196) \end{pspicture}$
The side of a regular hexagon has the same length as the radius of the circle circumscribing it. This fact is illustrated below.

$\begin{pspicture}(0,-0.2)(6,5.2) \pscircle[linecolor=cyan](3,2.598){3} \psline[l... ...s(3,2.598)(0,2.598)(1.5,0)(4.5,0)(6,2.598)(4.5,5.196)(1.5,5.196) \end{pspicture}$

From the last remark, it is easy to see that a regular hexagon is constructible using compass and straightedge.

"hexagon" is owned by Wkbj79. [ full author list (4) | owner history (3) ]

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