The Golden Rectangle

A rectangle with its sides in the 'Golden Ratio' or 1 : 1.618...
Try this Drag the orange dots on each vertex to reshape the rectangle. Note that its sides always remain in the 'golden ratio'.

The Golden rectangle has been known since antiquity as one having a pleasing shape, and is frequently found in art and architecture as a rectangular shape that seems 'right' to the eye. It is mentioned in Euclid's Elements and was known to artists and philosophers such as Leonardo da Vinci.

One of the interesting properties of the golden rectangle is that if you cut off a square section whose side is equal to the shortest side, the piece that remains is also a golden rectangle.

In the figure below, the yellow rectangle is in the same proportion as the original larger rectangle after the gray square is cut off. Both the rectangles ABCD and PBCQ are golden rectangles.

Golden rectangle showing that cutting off a square produces another golden rectangle

Other polygon topics


Types of polygon

Area of various polygon types

Perimeter of various polygon types

Angles associated with polygons

Named polygons