Octagram calculator
Calculator and formulas for calculating an octagram
This function calculates various parameters of an octagram.
To perform the calculation, select the property you know from the pull down menu and enter its value. Then click the 'Calculate' button.
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Drawing an octagram
First, an octagon (an octagonal polygon) is drawn. Then the corners of the octagon are connected by skipping two corners at a time and connecting every third. The lines between the corners of the octagon then form the regular octagram.
Octagram formulas
Side length of the octagon (\(\small{a}\))
\(\displaystyle a = (\sqrt{2} - 1) · l\;\;\; ≈0.4142·l\)
Side length of the spike (\(\small{b}\))
\(\displaystyle b=\frac{2-\sqrt{2}}{2} · l\;\;\; ≈0.2929·l\)
Diagonal (\(\small{d}\))
\(\displaystyle d=\sqrt{4+2·\sqrt{2}} · a\;\;\; ≈2.613·a\)
Chord length (\(\small{l}\))
\(\displaystyle l=a+2 ·b\)
Area (\(\small{A}\))
\(\displaystyle A= (6· \sqrt{2} - 8) · l^2 \;\;\; ≈0.4853· l^2\)
Perimeter (\(\small{P}\))
\(\displaystyle P= 16·b\)
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