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Equiangular surfaces, self-similar surfaces, and the geometry of seashells. (English) Zbl 1245.53009
From the summary: One of the most fascinating curves in the plane is the logarithmic spiral, also known as the equiangular spiral. Among its interesting properties is the fact that it is self-similar. In this article, we explore three-dimensional versions of these two properties: surfaces that are equiangular and those that are self-similar. It will be seen that the two concepts are independent in three dimensions but not in two. Among equiangular surfaces, there are some that are self-similar, but also some that are not. Furthermore, there are self-similar surfaces that are not equiangular. We give examples of all three types.

53A04 Curves in Euclidean and related spaces
53A05 Surfaces in Euclidean and related spaces
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