Drawing Instrument, Trimetric Ruler

Description:

James Sutherland Frame, chairman of the mathematics department at Michigan State University, wished to assist students in drawing useful projections of three-dimensional objects in a two-dimensional plane. In particular, he wanted them to draw axiometric projections, that as to say, to represent an object by a single projection on a plane so chosen as not to be perpendicular to any of the important lines of the object. To that end, he invented this device, which he called a trimetric ruler.

This flat painted wooden instrument has three edges marked with appropriate scales, so that unit vectors along three mutually perpendicular axes in space are represented in an orthographic projection (a projection in which lines of projection are parallel and perpendicular to the projection plane) by units measured on the three scales and directed along the corresponding edges of the instrument. To plot points with the device, one edge is always kept vertical and the three coordinates of the points are measured along the three scales of the ruler. The ruler allows one to draw complicated figures quickly and easily in parallel projection.

A mark on the object reads: Pat App For.

Frame (1907-1997) was born in New York City, and educated at Harvard University. He taught at Brown University and at Allegheny College before moving to Michigan State University (then Michigan Agricultural College) as chair of the Department of Mathematics in 1943. He remained department chair until 1960 and retire in 1977. Frame described his trimetric ruler at the Annual Meeting of the Michigan Section of the Mathematical Association of America in April 1946 and included an example of it in each copy of a textbook on solid geometry that he published two years later. He apparently did not receive a patent for the instrument.

References:

James S. Frame, Solid Geometry, New York: McGraw-Hill, 1948, esp. pp. 6-7, 72, 241-245.

"Annual Meeting of the Michigan Section," American Mathematical Monthly, 54 #1, January, 1947, pp. 69-71.

Dick Phillips, "J. Sutherland Frame Honored," Newsletter of the Michigan Section of the MAA, Fall, 1997.