The Introduction and Spread of Nomography in America, 1900-1950

Time: 6:00 p.m.

Place: Room 103, Mendel Science Center, Villanova University

Abstract: Nomography can be roughly defined as the theory and methods by which numerical evaluation of ordinary functional relations can be accomplished geometrically. (The slide rule is a simple example of one such method.) It was established as a mathematical discipline in 1899 by Maurice d'Ocagne (1862-1938), an accomplished French engineer who synthesized earlier work on this subject. His 1899 volume "Traite de Nomographie" is a systematic development of the construction and use of what came to be called nomograms (variously called charts, alignment diagrams, intersection diagrams, or abaques) for use in computations in diverse engineering disciplines. While the use of nomograms to aid in calculation became widespread in Europe in the following years, the mathematics associated with their construction received attention as well. This resulted in articles in mathematical journals and a mention of the field by Hilbert in connection with problem 13 of his list of 23 problems of 1900. Nomograms have been described by one writer as the "fractals of their day" due to their relation to mathematical law and visual appeal.

This talk attempts to survey how nomography was introduced into the United States in the years following the publication of d'Ocagne's book, looking at its debut in the various communities of mechanical, civil, and electrical engineers, scientists, and mathematicians, with special focus on the latter. During the period from 1900 to 1950 mathematicians such as Frank Morley, E. H. Moore, T. H. Gronwall, O. D. Kellogg, Lester Ford and Edward Kasner concerned themselves with popularizing, extending, and using the ideas of nomography. The subject was taught in colleges and technical institutes, often out of textbooks written by the instructors. It appealed to all types of mathematical people: pure researchers, college professors and high school teachers, and had its enthusiasts among algebraists, geometers and analysts. Nomograms became particularly popular as a graphical method for solving polynomial equations of degree five or less, and found a place in the changing nature of college algebra during this time. We also will mention some mathematical obstacles which occurred as they came into wider use in scientific, engineering and industrial settings.