From Golden Spirals to Constant Slope Surfaces

Abstract

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.

11 pages, 8 figures

References in corpus (1)

• Constant Angle Surfaces in $\H^2\times \R$

Cited by in corpus (4)

• Time-like constant slope surfaces and space-like Bertrand curves in Minkowski 3-space
• Concircular helices and concircular surfaces in Euclidean 3-space R3
• Golden Spiral Interferometry for Radio Astronomy. A proposal
• On weak r-Helix submanifolds