How to Construct a Golden Rectangle

Last Updated: May 13, 2021

A golden rectangle is a rectangle with side lengths that are in the golden ratio (about 1:1.618). This article also explains how to construct a square, which is needed to construct a golden rectangle.

Steps

1
Draw a square. Let us name the vertices of the square as A, B, C and D.^{[1]
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2
Locate the mid-point of any one side of the square by bisecting it. Let us pick the side AB and call its mid-point as point P.^{[2]
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3
Connect the mid-point P to a corner of the opposite side. Since P lies on the side AB, the opposite side shall be the side CD. Let's choose to connect P with C.
4
Place the tip of the compass on P and set its width to match the distance PC. Draw a large arc towards the side BC.^{[3]
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5
Extend the side AB to cut the arc at some point (say Q).^{[4]
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6
Draw a line parallel to the side BC, passing through the point Q.
7
Extend the side DC to meet the parallel line at some point (say R).^{[5]
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8
Congratulations! You just drew a Golden Rectangle AQRD. Erase any extraneous constructions if you so wish.
- You may verify that the ratio of the measure of the shorter side of the rectangle (QR or AD) to the measure of its longer side (AQ or RD) is very close to 1:1.618.

Community Q&A

Question

What tool is used to draw a rectangle?

Community Answer

You can make rectangles with a stencil, a ruler, or trace around a rectangular object.