page_title: Crockett Johnson
section_title: Mathematical Paintings
hierarchical_section_title: Crockett Johnson / Mathematical Paintings
caption_attribution_description: English: Painting. "Polar Line of a Point and a Circle (Apollonius)," by Crockett Johnson. 1979.1093.26.DESCRIPTION In 1966, Crockett Johnson carefully read Nathan A. Court's book College Geometry, selecting diagrams that he thought would be suitable for paintings. In the chapter on harmonic division, he annotated several figures that relate to this painting. The work shows two orthoganol circles, that is to say two circles in which the square of the line of centers equals the sum of the squares of the radii. A right triangle formed by the line of centers and two radii that intersect is shown. The small right triangle in light purple in the painting is this triangle. Crockett Johnson's painting combines a drawing of this triangle with a more complex figure used in a discussion of further properties of lines drawn in orthoganal circles. In particular, suppose that one draws a line segment from a point outside a circle that intersects it in two points, and selects a fourth point on the line that divides the segment harmonically. For a single exterior point, all these such points lie on a single line, perpendicular to the line of centers of the two circles, which is called the polar line. The painting is #38 in the series. It has a background in two shades of cream, and a light tan wooden frame. It shows two circles that overlap slightly and have various sections. The circles are in shades of blue, purple and cream. The painting is signed: CJ66. References: Nathan A. Court, College Geometry (1964 printing), p. 175–78. This volume was in Crockett Johnson's library. T. L. Heath, ed., Apollonius of Perga: Treatise on Conic Sections (1961 reprint). This volume was not in Crockett Johnson's library.
context_page_description: Crockett Johnson was the pen name of the American cartoonist and children's book illustrator David Johnson Leisk. He is best known for the comic strip Barnaby and the Harold series of books beginning with Harold and the Purple Crayon.
  From 1965 until his death Johnson created over a hundred paintings relating to mathematics and mathematical physics. Eighty of these are found in the collections of the National Museum of American History.
context_section_description: Johnson created his series of more than 100 mathematical paintings inspired by geometric principles and mathematicians. He painted layered geometric shapes in the paintings, based on classic mathematical theorems and diagrams in James Newman’s The World of Mathematics as well as other mathematics books. Later, he began to construct using his own inventions. Most of Johnson's abstract images are painted with house paint on the rough side of a two-by-three foot piece of masonite, save those he enlarged to four-by-four, he explained in a letter.
  Johnson made an effort to differentiate his paintings from contemporary art in that his are based on the mathematics of geometry, not solely the shapes. In his 1971 article titled "Geometric Geometric Painting," published in Leonardo, Johnson describes this type of geometric painting as using shapes and lines to experiment with color and optic illusion for decoration, the evocation of emotion, representation of ancient symbols or other purposes unrelated to geometry.
caption: "Polar Line of a Point and a Circle (Apollonius)"
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