Star of Lakshmi calculator
Calculator and formulas for calculating a Star of Lakshmi
This function calculates various parameters of a Star of Lakshmi.
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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Description of the Star of Lakshmi
The Star of Lakshmi is a geometric figure. It consists of an eight-pointed star, which is created by superimposing two congruent squares, which are rotated 45 degrees relative to each other. This unique symbol is closely associated with the Hindu goddess Lakshmi, who is revered as a giver of prosperity and wealth. The eight points of the star represent the Ashtalakshmi, which symbolize various forms of abundance and blessings.
Formulas for the star of Lakshmi
Edge length of the square (\(\small{a}\))
\(\displaystyle a=2 · c+b\)
Edge length of the octagon (\(\small{b}\))
\(\displaystyle b= (\sqrt{2}-1) ·a\)
Edge length of the star (\(\small{c}\))
\(\displaystyle c= \frac{(2 - \sqrt{2}) · a}{2}\)
Chord length (\(\small{l}\))
\(\displaystyle l = 2 ·c · cos\left(\frac{π}{8}\right)\)
Perimeter (\(\small{P}\))
\(\displaystyle P = 16 · c\)
Area of the octagon (\(\small{Ao}\))
\(\displaystyle Ao = 2 · (\sqrt{2} - 1) · a^2\)
Area of the star (\(\small{As}\))
\(\displaystyle As = 2 · (2 - \sqrt{2}) · a^2\)
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