René Descartes’ method for finding tangents (equivalently, subnormals) depends on geometric and algebraic properties of a family of circles intersecting a given curve. It can be generalized to establish a calculus of subnormals, an alternative to the calculus of Newton and Leibniz. Here we prove subnormal counterparts of the well-known differentiation rules of the calculus.
Greg Boudreaux (email@example.com) obtained a Ph.D. from the University of Louisiana at Lafayette in 2001. He is currently an associate professor of mathematics at the University of North Carolina at Asheville, where his research interests include abstract algebra, cryptology, and math history. Outside the classroom, he has a passion for gardening, with a special fondness for carnivorous plants from Louisiana, his home state.
Jess Walls (firstname.lastname@example.org) earned a B.A. in applied mathematics from the University of North Carolina at Asheville in 2006. He currently works as a programmer in Raleigh. When not in the office, he enjoys number theory and the company of his great dane.