A new mathematical discovery – the orthovolute – was recently made in Richard Palmaccio’s Multivariable Calculus class. After completing an in-depth study of the cycloid, a test on parametric equations was given and one of the problems led to this discovery of a new kind of locus of points situation described by two curves related to a given curve. One student, Charles Yang ‘22, ran with the concept of the orthovolute and was the first to complete the derivation of the orthovolute for the cycloid. He then introduced Palmaccio to the Desmos graphing system. Figure 12 was the result of Charles’ work. The remaining students, Alessandro Barbiellini ‘21, Matthew Choi ‘22, Daniel Ko ‘21, and Samuel Randall ‘21, are also, in addition to Charles, accomplished mathematicians who are among the very few to have ascended to Multivariable Calculus while still in high school.
Palmaccio, a 1962 graduate of St. Sebastian's and veteran teacher of 54 years, has taught many classes of varying levels of sophistication at St. Sebastian’s and notes that this present class in Multivariable Calculus ranks at the top of the many classes experienced. “Teaching this class of excellent mathematical scholars has been personally inspiring and has led in no small part to the creation of the orthovolute,” shared Palmaccio. An expert mathematician himself, Palmaccio’s problem inventions have been the basis of three past books, presenting some unique problem situations not available in ordinary textbooks.