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Thursday, February 17, 2011 - 6:00pm

Alan Gluchoff

Villanova University

Location

Villanova University

103 Mendel Hall

Light homemade supper available at 6 p.m. for $10 (optional)

Nomography can be defined as the study and preparation of graphical representations of mathematical equations. These representations usually take the form of charts or diagrams from which the values of certain variables in the relation can be read once others have been given. The subject has a history which goes back several centuries and is closely tied with engineering applications. It was organized as a body of knowledge by Maurice d’Ocagne, a French engineer, at the turn of the twentieth century. Nomography then spread to other countries, including America, in later years, where it became of use to engineers and scientists, and of interest to mathematicians. From an American Nomography text of 1947 used at MIT comes the following quote: “The theory of the nomgraphic chart cannot be dismissed as a simple topic. Mathematicians who do so are unaware that a complete treatment of the subject draws on every aspect of analytic, descriptive, and projective geometries, the several fields of algebra, and other mathematical fields.” This suggests a conflict over the status of nomography as a mathematical area: how deep is the mathematics of this subject? Is it more than just a set of techniques for drawing charts? Can nomography give rise to problems of genuine mathematical interest? We will examine these questions as they presented themselves to American mathematicians of the era 1900-1950 and give examples of the connections between nomography and: elementary properties of determinants, the duality principle of projective geometry, classification problems in elementary algebraic forms, finding roots of real polynomials, simple partial differential equations, cubic curves, and Hilbert’s thirteenth problem (number of examples to be limited by time constraints). An attempt will be made to determine how American mathematicians of this era felt about the mathematical status of nomography.