Spherical circles and constant angle surfaces

Abstract

In this present paper, we obtain a general version of constant angle surfaces constructed concerning any direction in three dimensional Euclidean space. This constant angle surface is the special case of developable ruled surfaces whose direction is a spherical circle. Here, we obtain the constant angle surfaces by taking the circles (small circles) whose radius is less than the radius of the sphere, as the base curve. Also, the relationship between the isophote curve and this surface and its physical interpretation is mentioned. When we beam from a light source in a constant direction, the intensity of the light will be the same at every point on this constant angle surface. This study is very important in terms of associating optics, a branch of physics, with geometry, a branch of mathematics. Finally, we classify the singular points of these constant angle surfaces.