# Painting - Nine-Point Circle

Description:

Although 18th- and 19th-century mathematicians were much interested in analysis and algebra, they continued to explore geometrical constructions. In 1765, the eminent Swiss-born mathematician Leonhard Euler showed that nine points constructed from a triangle lie on a circle. This circle would come to be called the Feuerbach circle after Karl Wilhelm Feuerbach, a professor at the gymnasium in Erlangen, Germany. In 1822, he published a paper explaining and proving the theorem.

It seems likely that the direct inspiration for this painting was a figure in H. S. M. Coxeter’s The Real Projective Plane (1955). A diagram on p. 143 of this book shows a triangle with its respective nine points. In his copy of the book, Crockett Johnson connected the points himself, thereby completing the circle (see the annotated figure). In addition, Johnson also annotated a figure in Nathan A. Court’s College Geometry (1964 printing), p. 103. Crockett Johnson's painting does not directly imitate either drawing, but it is evident that he studied each figure in creating his own construction.

The first three points of the nine-point circle are the midpoints of the sides of triangle QRP (points L, M, and N in the annotated drawing). The second three points are the bases of the altitudes of the triangle (points A, B, C). These altitudes meet at a point (S). The midpoints of the lines joining the vertices of the triangle to the intersection of the altitudes create the last three points that indicate the nine-point circle (L’, M’, N’).

The segments of the triangle that are not part of the circle are colored in shades of blue and gray. Those segments that are part of the circle are white and various shades of pink and yellow. The painting has a background defined by two shades of gray.

This oil painting on masonite, #75 in the series, dates from 1970, is signed in the upper left corner : CJ70. It is inscribed on the back: NINE-POINT CIRCLE (/) Crockett Johnson 1970. There is a metal frame.

Date Made: 1970

Painter: Johnson, Crockett

Location: Currently not on view

See more items in: Medicine and Science: Mathematics, Science & Mathematics, Crockett Johnson, Art

Exhibition:

Exhibition Location:

Credit Line: Ruth Krauss in memory of Crockett Johnson

Data Source: National Museum of American History

Id Number: 1979.1093.49Catalog Number: 1979.1093.49Accession Number: 1979.1093

Object Name: painting

Physical Description: masonite (substrate material)metal (frame material)Measurements: overall: 62.8 cm x 104.2 cm x 3.2 cm; 24 3/4 in x 41 in x 1 1/4 inoverall: 43 in x 2 in x 28 in; 109.22 cm x 5.08 cm x 71.12 cm

Record Id: nmah_694673

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