Painting - Fluxions (Newton)

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In the 17th century, the natural philosophers Isaac Newton and Gottfried Liebniz developed much of the general theory of the relationship between variable mathematical quantities and their rates of change (differential calculus), as well as the connection between rates of change and variable quantities (integral calculus).
Newton called these rates of change "fluxions." This painting is based on a diagram from an article by H. W. Turnbull in Newman's The World of Mathematics. Here Turnbull described the change in the variable quantity y (OM) in terms of another variable quantity, x (ON). The resulting curve is represented by APT.
Crockett Johnson's painting is based loosely on these mathematical ideas. He inverted the figure from Turnbull. In his words: "The painting is an inversion of the usual textbook depiction of the method, which is one of bringing together a fixed part and a ‘moving’ part of a problem on a cartesian chart, upon which a curve then can be plotted toward ultimate solution."
The arc at the center of this painting is a circular, with a tangent line below it. The region between the arc and the tangent is painted white. Part of the tangent line is the hypotenuse of a right triangle which lies below it and is painted black. The rest of the lower part of the painting is dark purple. Above the arc is a dark purple area, above this a gray region. The painting has a wood and metal frame.
This oil painting on pressed wood is #20 in the series. It is unsigned, but inscribed on the back: Crockett Johnson 1966 (/) FLUXIONS (NEWTON).
References: James R. Newman, The World of Mathematics (1956), p. 143. This volume was in the library of Crockett Johnson. The figure on this page is annotated.
Crockett Johnson, "On the Mathematics of Geometry in My Abstract Paintings," Leonardo, 5 (1972): pp. 97–8.
Currently not on view
National Museum of American History
Newton, Isaac
Johnson, Crockett
Credit Line
Ruth Krauss in memory of Crockett Johnson
Physical Description
masonite (substrate material)
wood (frame material)
metal (frame material)
overall: 121.5 cm x 120 cm x 3.8 cm; 47 13/16 in x 47 1/4 in x 1 1/2 in
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Crockett Johnson
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