Painting - Rectangles of Equal Area (Pythagoras)

Crockett Johnson used a wide range of geometrical constructions as the basis for his paintings. This painting is based on a method of constructing a rectangle equal in area to a given rectangle, given one side of the rectangle to be constructed.
In the painting, suppose that the cream-colored rectangle on the bottom left is given, as well as a line segment extending from the upper right corner of it. Construct the small triangle on the upper left. Draw the three horizontal lines shown, as well as the diagonal of the rectangle constructed. Extend this diagonal until it meets the bottom line, creating another triangle. The length of the base of this triangle will be the side of the rectangle desired. This rectangle is on the upper right in the painting.
This construction has been associated with the ancient Pythagoreans. Crockett Johnson may well have learned it from Evans G. Valens, The Number of Things. The drawing on page 121 of this book is annotated, although the annotations are faint.
The oil painting is #48 in the series. It has a black background and a black wooden frame, with the two equal triangles in light shades. The painting is signed on the front: CJ69. It is signed on the back: RECTANGLES OF EQUAL AREA (/) (PYTHAGORAS) (/) Crockett Johnson 1969.
Currently not on view
Object Name
date made
Johnson, Crockett
Physical Description
masonite (substrate material)
wood (frame material)
overall: 124 cm x 88.3 cm x 2.5 cm; 48 13/16 in x 34 3/4 in x in
ID Number
catalog number
accession number
Science & Mathematics
Crockett Johnson
See more items in
Medicine and Science: Mathematics
Crockett Johnson
Data Source
National Museum of American History, Kenneth E. Behring Center
Credit Line
Ruth Krauss in memory of Crockett Johnson
Additional Media

Visitor Comments

2/11/2016 11:27:06 AM
Very beautiful colors!I am a teacher in Greece and the problem of equal areas is very good for my students(16 years old) in Euclidian Geometry!Thank you...
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