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Drawing a Golden Rectangle

October 21st, 2009 by Math Tricks | Filed under Golden Rectangle, Mathematics Concepts.

Drawing A Golden Rectangle

Drawing a golden rectangle is pretty easy using the technique I will show you here.  I used PowerPoint to draw the rectangle here, but you can use this technique to draw a golden rectangle with just about any drawing program.  If you have a compass and a protractor, then I suggest that you try to draw your rectangle on paper.

First, draw a square.  You do not need to know the dimensions of the square, just be sure that all the sides are of equal length:

making a golden rectangle 1

Next, find the midpoint at the base of the square, and draw a line from the midpoint to the upper-right corner of the square:

making a golden rectangle 2

Now draw a circle with the midpoint of the base as the center.  Expand the circle such that the line from the base midpoint to the upper-right corner is a radial line from the center of the circle to the circle’s edge:

making a golden rectangle 3Now rotate the radial line downward, keeping the edge of the line on the circle:

making a golden rectangle 4Continue with the rotation until the radial line is parallel to the base of the square:

making a golden rectangle 5Remove the circle.  What is left is the square with an extension at the base:

making a golden rectangle 6Draw a rectangle around the base + extension and square height:

making a golden rectangle 7Finally, remove the extension and square.  What is left is a perfect golden rectangle:

making a golden rectangle 8Very easy and neat.  Congratulations, now you can create great works of art by incorporating golden rectangles into you masterpieces!

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2 Responses to “Drawing a Golden Rectangle”

  1. Kelvin | 12/04/10

    This technique is great however how can you mathematically or geometrically proof its correctness.

  2. SV | 29/05/13

    This was really helpful! Thanks

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