From Golden Spirals to Constant Slope Surfaces

By Marian Ioan Munteanu. 2009

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In this paper, we find all constant slope surfaces in the Euclidean 3-space, namely those surfaces for which the position vector of a point of the surface makes constant angle with the normal at the surface in that point. These surfaces could be thought as the bi-dimensional analogue of the generalized helices. Some pictures are drawn by using the parametric equations we found.

Subfields: Applied Mathematics, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/97ffe11b5c2cadedc0a6fd8f6ef7ddcdc78f66eb