Painting - Transversals (Ceva)

A transversal is a line that intersects a system of other lines or line segments. Here Crockett Johnson explores the properties of certain transversals of the sides of a triangle. The Italian mathematician Giovanni Ceva showed in 1678 that lines drawn from a point to the vertices of a triangle divide the edges of the triangle into six segments such that the product of the length of three nonconsecutive segments equals the product of the remaining three segments.

This painting shows a triangle (in white), lines drawn from a point inside the triangle to the three vertices, and a line drawn from a point outside the triangle (toward the bottom of the painting) to the three vertices. Segments of the sides of the triangle to be multiplied together are of like color. Crockett Johnson's painting combines two diagrams on page 159 of Nathan Court's College Geometry (1964 printing). These diagrams are annotated in his copy of the volume. Several of the triangles adjacent to the central triangle were used by Court in his proof of Ceva's theorem.

The painting is #31 in the series. It is signed: CJ66. There is a wooden frame painted off-white.

Currently not on view