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# Painting - Point Collineation in the Triangle (Euler)

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Description
Leonhard Euler (1707–1783) was the most prolific mathematician of the eighteenth century. He made significant contributions to geometry, calculus, mechanics, and number theory. He produced more than 800 publications during his lifetime, almost half of which were dictated after his eyesight failed in 1766. While Euler is best remembered for his contributions to analysis and mechanics, his interests included geometry. This figure illustrates a theorem about triangles associated with his name.
Euler showed that three points related to a triangle lie on a common line. The first is the circumcenter (point O in the figure), the intersection of the perpendicular bisectors of the three sides. This point is the center of the circle which passes through the vertices of the triangle. Johnson also constructed the three medians of the triangle and the three altitudes of the triangle. The medians intersect in a common point (point N in the figure) and the altitudes meet at a third point (H in the figure). These three points, Euler showed, lie on the same line. In the painting, Crockett Johnson also constructed the circle that circumscribes the triangle, as well as a circle of half the radius known as the nine-point circle. For a full description of this circle, see painting #75 (1979.1093.49).
In the painting, the circumcircle is centered exactly on the backing, and the Euler line extends from the lower right corner to the upper left corner. This divides the work into two triangles of equal area. The right half of the painting was executed in shades of red and purple, while the left half of the painting was executed in shades of gray and black. Crockett Johnson also joined the nine points of the nine-point circle to form an irregular polygon.
This oil painting on masonite is #28 in the series. There is a wooden frame painted black. The work was completed in 1966 and is signed: CJ66. It is signed on the back: Crockett Johnson 1966 (/) POINT COLLINEATION IN THE TRIANGLE (/) (EULER). For a related painting, see #75 (1979.1093.49).
Reference: Nathan A. Court, College Geometry (1964 printing), p. 103, cover. The figure on p. 103 is annotated.
Location
Currently not on view
Object Name
painting
1966
referenced
Euler, Leonhard
painter
Johnson, Crockett
Physical Description
masonite (substrate material)
wood (frame material)
Measurements
overall: 84.5 cm x 84 cm x 3.8 cm; 33 1/4 in x 33 1/16 in x 1 1/2 in
ID Number
1979.1093.20
catalog number
1979.1093.20
accession number
1979.1093
Credit Line
Ruth Krauss in memory of Crockett Johnson
See more items in
Medicine and Science: Mathematics
Science & Mathematics
Art
Crockett Johnson
Data Source
National Museum of American History
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