#
Mathematical Paintings of Crockett JohnsonResources

### Selected Works of David Crockett Johnson

*Barnaby*, New York, NY: Henry Holt and Company, 1943.

*Barnaby and Mr. O’Malley*, New York: Henry Holt and Company, 1944.

*Harold and the Purple Crayon*, New York: Harper 7 Row, 1955.

“A Geometrical Look at vp,”

*Mathematical Gazette*, 54 (Feb 1970): 59-60.

“On the Mathematics of Geometry in My Abstract Paintings,”

*Leonardo*, 5 (1972): 97-101.

“A construction for a regular heptagon,”

*Mathematical Gazette*, 17 (March 1975): 17-21.

Papers of Crockett Johnson, Mathematics Collections, National Museum of American History, Smithsonian Institution.

Correspondence in the Harley Flanders Papers, Mathematics Collections, National Museum of American History.

Correspondence in the Ad Reinhardt Papers, Archives of American Art, Smithsonian Institution.

### Selected Works about Crockett Johnson

Stephanie Cawthorne and Judy Green, “Cubes, Conic Sections, and Crockett Johnson,” *Convergence*, vol. 11, 2014. http://www.maa.org/publications/periodicals/convergence/cubes-conic-sections-and-crockett-johnson

Stephanie Crawthorne and Judy Green, “Harold and the Purple Heptagon,” *Math Horizons* (September 2009): 5-9.

Philip Nel, “Crockett Johnson and the Purple Crayon: A Life in Art,” *Comic Art*, 5 (2004): 2-18.

Philip Nel. *Crockett Johnson and Ruth Krauss: A Biography*, Jackson: University Press of Mississippi, in preparation.

James B. Stroud, “Crockett Johnson's Geometric Paintings,” *Journal of Mathematics and the Arts*, 2 #2 (June 2008): 77-99.

For a more detailed bibliography and further information, see the Crockett Johnson Web site created and maintained by Philip Nel.

For a description of American mathematics and science education at the time of Crockett Johnson’s paintings, see the Museum's Web site: “Mobilizing Minds: Teaching Math and Science in the Age of Sputnik.”

### Credits

This introduction and the accounts of Crockett Johnson paintings given below have benefited from insights of Uta C. Merzbach, Judy Green, J. B. Stroud, Philip Nel, Mark Kidwell, Emmy Scandling, and Joan Krammer.

"Mathematical Paintings of Crockett Johnson - Resources" showing 4 items.

## Painting -

*Pendulum Momentum (Galileo)*- Description
- The Greek mathematician Aristotle, who lived from about 384 BC through 322 BC, believed that heavy bodies moved naturally downward, while lighter substances such as air naturally ascended. Other forms of terrestrial motion required a sustaining force, which was not expressed mathematically. The Italian Galileo Galilei (1564–1642) challenged Aristotle. He held that motion was persistent and would continue until acted upon by an opposing, outside force.

- In a book entitled
*Dialogues Concerning the Two Chief World Systems*, Galileo presented his ideas in a dispute between three men: Salviati, Sagredo, and Simplicio. Salviati, a spokesman for Galileo, explained his revolutionary ideas, one of which is illustrated by a diagram that was the basis for this painting. This image can be found in Crockett Johnson's copy of*The World of Mathematics*, a book by James R. Newman. It is probable that this image served as inspiration for this painting, although Johnson did not annotate this diagram.

- In Galileo's
*Dialogues*, Salviati argued that if a lead weight is suspended by a thread from point A (see figure) and is released from point C, it will swing to point D, which is located at the same height as the initial point C. Furthermore, Salviati stated that if a nail is placed at point E so that the thread will snag on it, then the weight will swing from point C to point B and then up to point G, which is also located at the same height as the initial point C. The same occurs if a nail is placed at point F below the line segment CD.

- The painting is executed in purple that progresses from light tints to darker shades right to left. This gives the figure a sense of motion akin to that of a pendulum. The background is washed in gray and black. The line created by the initial and final height of the weight divides the background.

*Pendulum Momentum*, a work in oil on masonite, is painting #13 in the Crockett Johnson series. It was executed in 1966 and is signed: CJ66. There is a wooden frame painted black.

- Location
- Currently not on view

- date made
- 1966

- referenced
- Galilei, Galileo

- painter
- Johnson, Crockett

- ID Number
- 1979.1093.08

- catalog number
- 1979.1093.08

- accession number
- 1979.1093

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Painting -

*Velocity on Inclined Planes (Galileo)*- Description
- This oil painting is based on a figure from Galileo Galilee's
*Dialogues Concerning Two New Sciences*(1638), Book 3. Here Galileo discussed the time of descent of bodies rolling without friction along inclined planes. He argued that if from the highest point in a vertical circle there be drawn any inclined planes meeting the circumference of the circle, the times of descent along these chords are equal to one another. This painting shows two inclined planes drawn from the highest point of a vertical circle, with a ball moving along each chord. Crockett Johnson probably became familiar with Galileo's figure by examining the translation of part of his book published in James R. Newman,*The World of Mathematics*, vol. 2, New York: Simon and Schuster, 1956, p. 751–52. This volume was in Crockett Johnson's library. The figure on p. 752 is annotated.

- The painting has a gray background and a metal and wooden frame. It shows two superimposed triangles (inclined planes), one reddish purple, and the other smaller one blue. Both of these triangles are inscribed in the same white circular arc. A light purple circle is shown near the bottom of the purple triangle, and a light blue circle near the bottom of the blue triangle.

- The work is # 42 in the series. It is signed: CJ66. Compare to paintings #96 (1979.1093.64) and #71 (1979.1093.46).

- Location
- Currently not on view

- date made
- 1966

- referenced
- Galilei, Galileo

- painter
- Johnson, Crockett

- ID Number
- 1979.1093.30

- catalog number
- 1979.1093.30

- accession number
- 1979.1093

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Painting -

*Law of Motion (Galileo)*- Description
- Crockett Johnson based this painting on the discussion of motion along inclined planes by Galileo Galilee in his
*Dialogues Concerning Two New Sciences*(1638). Here Galileo showed that if from a fixed point straight lines be extended indefinitely downwards and a point be imagined to move along each line at a constant speed, all starting from the fixed point at the same time and moving with equal speeds, the locus of the moving points will be an expanding circle.

- This painting shows four superimposed circles in various shades of gray, white and black. These circles all have a common point at the center top, and differ in radius. They are shaded into several regions which are divided by lines originating at the common point. The work has an orange background and a black wooden frame. It is probably based on a drawing in E. G. Valens,
*The Attractive Universe*(1969). This volume is in Crockett Johnson's library, annotated on the page indicated.

- The painting is #71 in the series. It is signed: CJ70.

- References: Galileo Galilee,
*Dialog Concerning Two New Sciences, Third Day*(Figure 59 in the Dover edition).

- E. G. Valens,
*The Attractive Universe: Gravity and the Shape of Space*, Cleveland and New York: World Publishing Company, 1969, p. 135.

- Location
- Currently not on view

- date made
- 1970

- referenced
- Galilei, Galileo

- painter
- Johnson, Crockett

- ID Number
- 1979.1093.46

- catalog number
- 1979.1093.46

- accession number
- 1979.1093

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Painting -

*Velocities and Right Triangles (Galileo)*- Description
- This is the third painting by Crockett Johnson to represent the motion of bodies released from rest from a common point and moving along different inclined planes. In the
*Dialogues Concerning Two New Sciences*(1638), Galileo argued that the points reached by the balls at a given time would lie on a circle. Two such circles and three inclined planes, as well as a vertical line of direct fall, are indicated in the painting. One circle has half the diameter of the other. Crockett Johnson also joins the base of points on the inclined planes to the base of the diameters of the circles, forming two sets of right triangles.

- This oil painting on masonite is #96 in the series. It has a black background and a wooden and metal frame. It is signed on the back: VELOCITIES AND RIGHT TRIANGLES (GALILEO) (/) Crockett Johnson 1972. Compare to paintings #42 (1979.1093.30) and #71 (1979.1093.46), as well as the figure from Valens,
*The Attractive Universe: Gravity and the Shape of Space*(1969), p. 135.

- Location
- Currently not on view

- date made
- 1972

- referenced
- Galilei, Galileo

- painter
- Johnson, Crockett

- ID Number
- 1979.1093.64

- catalog number
- 1979.1093.64

- accession number
- 1979.1093

- Data Source
- National Museum of American History, Kenneth E. Behring Center