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Boyadzhiev presents at the BIOMATH 2012 International Conference

Khristo Boyadzhiev, professor of mathematics and statistics, presented a paper, “Equiangular Spirals, Equiangular Surfaces and Self-similar Surfaces in Biology,” at the BIOMATH 2012 International Conference held June 17-22 in Sofia, Bulgaria.  

The equiangular spiral is used to explain the trajectories of insects orientating themselves with respect to a light source. There are two independent properties that characterize the logarithmic spiral. The first property is that it is self-similar, that is, it is proportional to itself.  The second property is that it is equiangular which means that at every point of the curve the radius vector and the normal vector cut one and the same angle.  

Boyadzhiev also presented examples showing the interplay of the properties of self-similarity and equiangularity for surfaces in three dimensions.