Golden rectangle
Step-by-Step Construction of a Golden Rectangle
Use the buttons in the app below to explore the construction of a golden rectangle.
When the construction is done, drag points A and B and observe how the ratio of the lengths of the rectangle sides is always equal to the golden number
Try It Yourself...
In the app below, there is a golden rectangle, constructed exactly as described in the previous app.
You already know that the ratio between side and side of the rectangle is constant and equal to (the golden ratio).
Imagine removing the square from the rectangle, and consider the remaining rectangle .
Measure the lengths of its sides using GeoGebra tools, then calculate the ratio between the longer side and the shorter side.
What do you observe?
Describe the results that you have obtained.
With GeoGebra...
Use GeoGebra's tools to build another golden rectangle, starting from the square with side . When done, imagine to remove the square you have built, then measure the sides of the remaining rectangle and calculate their ratio. What do you observe?
A Golden Property!
Subtracting from a golden rectangle a square with a side equal to the shorter side of the rectangle produces another golden rectangle.
And the ratio between the sides of two consecutive squares removed from the golden rectangle is golden!