Consider the following process: start with a rectangle, inscribe a square so that the the square shares a side with one of the shorter sides of the rectangle, then consider the remaining region of the rectangle. This is a new rectangle (though if the original shape was itself a square, this rectangle will be empty).
A rectangle is a golden rectangle if the new rectangle is similar to the original one.
All golden rectangles are similar to each other, and the golden ratio is the ratio of its side lengths. It is commonly denoted by .
Numerically, the golden ratio is the positive solution to the quadratic , which is: