Mathematics Seminar: The Power of Padovan

The Fibonacci (or Pingala) numbers are the single most famous number sequence in music, art, and architecture. They arise naturally in both a spiral of squares and a ratio involving proportions of rectangles. In this talk, we question how natural the choices in both these constructions are, and focus on a different sequence which arises as a result of both a different spiral and a different question about proportions of rectangles. We construct this new sequence in both ways and provide ample evidence for its importance alongside its more famous cousin.

We will show how our new sequence surprisingly appears in Pascal's triangle and then prove several identities without either words or numbers, by considering colorings corresponding to sums of entries. We will examine the uses of this sequence in architecture, particularly in Hans van der Laan's Monastery at Vaals. Finally we will present recent research on the growth properties of this sequence, presenting a counterexample to a conjecture and seeing how far we can push the limits of that counterexample.

 

Speaker: David Nacin, William Paterson University

Date: Friday, September 18, 2020

Time: 3:30 p.m.

Please contact johanna.n.franklin@hofstra.edu for the zoom link.

 


Photo credit: Tim Miller | Courtesy of William Paterson University

Friday, September 18, 2020

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Hofstra University Virtual Event
Virtual
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Hempstead, NY 11549-1000


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