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squared based on center point and area
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How would you construct a square given its center point and area?
My first attempt:
• find the apothem:
apothem = sqrt(area) / 2
• create an apothem from center point A:
Segment[A, apothem]
• use the rotate tool three times to create the other apothems
• complete the square using lines parallel to the apothems
...other ideas? :]
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A shorter version:
c=circle[A,sqrt(area) / 2]
Polygon[point[c,0],point[c,0.25],4]
Regards Abakus
That's an interesting approach. I wasn't aware of the Point[ <Object>, <Parameter> ] variation.
Although it needs a small tweak to produce a square with the original area,
because it is based on the length of half a diagonal, instead of an apothem.
c=circle[A,sqrt(area)*sqrt(2)/2]
Polygon[point[c,0],point[c,0.25],4]
and for the other orientation:
Polygon[point[c,0.125],point[c,0.375],4]
abakus method is fast and easy.
Here are two other approaches (area= A, center = C):
a) using Zip command and polar coordinates:
Polygon[Zip[C + (sqrt(A / 2); X), X, {0, π/2, π, 3π/2}]]
b) using complex numbers multiplication:
Polygon[Sequence[C + (sqrt(A / 2) + 0ί) ℯ^(ί π / 2 k), k, 0, 3]]
Thanks for the ideas. 8)
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