Mathematical Paintings of Crockett Johnson - Introduction
"Mathematical Paintings of Crockett Johnson - Introduction" showing 2 items.
Painting - Conic Curve (Apollonius)
- Description
- In ancient times, the Greek mathematician Apollonius of Perga (about 240–190 BC) made extensive studies of conic sections, the curves formed when a plane slices a cone. Many centuries later, the French mathematician and philosopher René Descartes (1596–1650) showed how the curves studied by Apollonius might be related to points on a straight line. In particular, he introduced an equation in two variables expressing points on the curve in terms of points on the line. An article by H. W. Turnbull entitled "The Great Mathematicians" found in The World of Mathematics by James R. Newman discussed the interconnections between Apollonius and Descartes, and apparently was the basis of this painting. The copy of this book in Crockett Johnson's library is very faintly annotated on this page. Turnbull shows variable length ON, with corresponding points P on the curve.
- The analytic approach to geometry taken by Descartes would be greatly refined and extended in the course of the seventeenth century.
- Johnson executed his painting in white, purple, and gray. Each section is painted its own shade. This not only dramatizes the coordinate plane but highlights the curve that extends from the middle of the left edge to the top right corner of the painting.
- Conic Curve, an oil or acrylic painting on masonite, is #11 in the series. It was completed in 1966 and is signed: CJ66. It is marked on the back: Crockett Johnson 1966 (/) CONIC CURVE (APOLLONIUS). It has a wooden frame.
- Location
- Currently not on view
- date made
- 1966
- referenced
- Apollonius of Perga
- painter
- Johnson, Crockett
- ID Number
- 1979.1093.06
- catalog number
- 1979.1093.06
- accession number
- 1979.1093
- Data Source
- National Museum of American History, Kenneth E. Behring Center
Painting - Polar Line of a Point and a Circle (Apollonius)
- 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.
- Location
- Currently not on view
- date made
- 1966
- referenced
- Apollonius of Perga
- painter
- Johnson, Crockett
- ID Number
- 1979.1093.26
- catalog number
- 1979.1093.26
- accession number
- 1979.1093
- Data Source
- National Museum of American History, Kenneth E. Behring Center