# Professor Elllis-Monaghan presents beautiful objects in mathematics at AAAS meeting

Professor of mathematics Joanna Ellis-Monaghan presented her research "Mathematical Beauty in the Shapes of Sea Shells" at the annual meeting of the American Association for the Advancement of Science (AAAS) on Feb. 15 in Boston at the Hynes Convention Center.

From Feb. 14 through 18, Boston welcomed thousands of scientists, teachers and journalists for the 2013 annual meeting of the "triple-A S," the non-profit society that publishes the prestigious journal Science.

Professor Ellis-Monaghan described her presentation this way:

"Part of the natural beauty of seashell derives from the visual rhythm of their self-replicating whorls. We give a mathematical model that captures sea shell morphology using space curves, parameterized surfaces, and Frenet frames. We show how the growth parameters of this model may be measured from x-rays or cross sections of actual shells, and then 3-D computer generated simulations of the intact shell produced.

"We conclude with a gallery of 'fantasy' shells, that is, shells created solely for their artistic appeal, but which also demonstrate the effects of manipulating the parameters of the model.

"The basic shell model may be taught at the undergraduate level (e.g. calculus III, vector calculus, or differential geometry), and provides a beautiful and engaging introduction to mathematical modeling. It is available as a 'discovery-learning' module through ILAP/COMAP."

Professor Monaghan credits her colleagues Professors Declan McCabe, George Ashline, and Zsuzsanna Kadas with contributions to the study.

### Recipient of a Saint Michael's College faculty achievement award, Professor Ellis-Monaghan was cited this way:

"In her nine years as a faculty member at Saint Michael's College Jo has built an impressive research program that encompasses both her own theoretical research in Algebraic Combinatorics and Graph Theory, and a thriving program of interdisciplinary applied research that systematically incorporates research opportunities for undergraduates."

Professor Ellis-Monaghan has some 40 publication on her resume. She holds two patents and has developed computer software for industry and for the classroom. She does extensive outreach and collaboration with researchers in universities and in industry, as well as with students. In 2010, she held a visiting fellowship at the Isaac Newton Institute, Cambridge University in Cambridge, England.

Professor Ellis-Monaghan crafts her studies to include student research components. She has in the past half-dozen years created summer research groups that have generated new enthusiasm among students and have regularly resulted in student publications. Her guidance in grant- and course-related research has yielded more than 50 student presentations at events such as the Hudson River Conference, NASA programs, and regional mathematics meetings.

Professor Ellis-Monaghan is Editor-In-Chief of PRIMUS, a journal devoted to undergraduate mathematics, and she serves on the Academic Advisory Board for the computer algebra system, Maple.

**Grants:** Her work has received funding from the Vermont Genetics Network, VT-EPSCoR, the NASA-Vermont Space Grant Consortium, and the National Security Agency. Most recently, she received a three-year, $200,000 National Science Foundation research grant to support her work, with her colleague Greta Pangborn and student assistants, on "New Graph Theory from and for Nanoconstruct Design Strategies".

View Professor Ellis-Monaghan's Curriculum Vitae.

# Professor Elllis-Monaghan presents beautiful objects in mathematics at AAAS meeting

Professor of mathematics Joanna Ellis-Monaghan presented her research "Mathematical Beauty in the Shapes of Sea Shells" at the annual meeting of the American Association for the Advancement of Science (AAAS) on Feb. 15 in Boston at the Hynes Convention Center.

From Feb. 14 through 18, Boston welcomed thousands of scientists, teachers and journalists for the 2013 annual meeting of the "triple-A S," the non-profit society that publishes the prestigious journal Science.

Professor Ellis-Monaghan described her presentation this way:

"Part of the natural beauty of seashell derives from the visual rhythm of their self-replicating whorls. We give a mathematical model that captures sea shell morphology using space curves, parameterized surfaces, and Frenet frames. We show how the growth parameters of this model may be measured from x-rays or cross sections of actual shells, and then 3-D computer generated simulations of the intact shell produced.

"We conclude with a gallery of 'fantasy' shells, that is, shells created solely for their artistic appeal, but which also demonstrate the effects of manipulating the parameters of the model.

"The basic shell model may be taught at the undergraduate level (e.g. calculus III, vector calculus, or differential geometry), and provides a beautiful and engaging introduction to mathematical modeling. It is available as a 'discovery-learning' module through ILAP/COMAP."

Professor Monaghan credits her colleagues Professors Declan McCabe, George Ashline, and Zsuzsanna Kadas with contributions to the study.

### Recipient of a Saint Michael's College faculty achievement award, Professor Ellis-Monaghan was cited this way:

"In her nine years as a faculty member at Saint Michael's College Jo has built an impressive research program that encompasses both her own theoretical research in Algebraic Combinatorics and Graph Theory, and a thriving program of interdisciplinary applied research that systematically incorporates research opportunities for undergraduates."

Professor Ellis-Monaghan has some 40 publication on her resume. She holds two patents and has developed computer software for industry and for the classroom. She does extensive outreach and collaboration with researchers in universities and in industry, as well as with students. In 2010, she held a visiting fellowship at the Isaac Newton Institute, Cambridge University in Cambridge, England.

Professor Ellis-Monaghan crafts her studies to include student research components. She has in the past half-dozen years created summer research groups that have generated new enthusiasm among students and have regularly resulted in student publications. Her guidance in grant- and course-related research has yielded more than 50 student presentations at events such as the Hudson River Conference, NASA programs, and regional mathematics meetings.

Professor Ellis-Monaghan is Editor-In-Chief of PRIMUS, a journal devoted to undergraduate mathematics, and she serves on the Academic Advisory Board for the computer algebra system, Maple.

**Grants:** Her work has received funding from the Vermont Genetics Network, VT-EPSCoR, the NASA-Vermont Space Grant Consortium, and the National Security Agency. Most recently, she received a three-year, $200,000 National Science Foundation research grant to support her work, with her colleague Greta Pangborn and student assistants, on "New Graph Theory from and for Nanoconstruct Design Strategies".

View Professor Ellis-Monaghan's Curriculum Vitae.