squared based on center point and area

Derek S. shared this question 8 years ago
Answered

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? :-]

Comments (4)

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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? :-]

A shorter version:


c=circle[A,sqrt(area) / 2]

Polygon[point[c,0],point[c,0.25],4]


Regards Abakus

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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]

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1

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]]

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Thanks for the ideas. 8)

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