Golden rectangle

A golden rectangle is a rectangle whose side lengths are in the golden ratio, 1:φ, that is, approximately 1:1.618.

A distinctive feature of this shape is that when a square section is removed, the remainder is another golden rectangle, that is, with the same proportions as the first. Square removal can be repeated infinitely, which leads to an approximation of the golden spiral.

According to astrophysicist and math popularizer Mario Livio, since the publication of Luca Pacioli's Divina Proportione in 1509, when "with Pacioli's book, the Golden Ratio started to become available to artists in theoretical treatises that were not overly mathematical, that they could actually use," many artists and architects have proportioned their works to approximate the form of the golden rectangle, which has been considered aesthetically pleasing.

Constructing a golden rectangle

A method to construct a golden rectangle. The resulting dimensions are in the ratio 1:φ, the golden ratio.

1. Construct a simple square
2. Draw a line from the midpoint of one side of the square to an opposite corner
3. Use that line as the radius to draw an arc that defines the height of the rectangle
4. Complete the golden rectangle