A well-known property of the catenary curve is that the ratio of the area under the curve to
the arc length of the curve is independent of the interval over which these quantities are …

We classify hypersurfaces of revolution for which the principal curvatures are proportional.
These hypersurfaces form a one-parameter family indexed by the reals. The subsequent …

We generalize hypersurfaces of revolution by allowing the profile curve to be dependent on
more than one variable. We call these more general objects spherical arrays and we use …

First, we compute the volume of an n-dimensional ball B n ( r ) \documentclass[12pt]{minimal}
\usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} …

We define a family of curves, the n-catenaries, parameterized by the nonzero reals. They
include the classical catenaries (n= 1), parabolas (n= 1/2), cycloids (n=− 1/2), and …

Let H be a hypersurface in ℝ n and let π be an orthogonal projection in ℝ n restricted to H.
We say that H satisfies the Archimedean projection property corresponding to π if there …

We consider a variation of the classical Grazing Goat Problem and we explore connections
to a number of surprising properties of spheres, including the curious volume-accumulation …

We show that the n-dimensional equizonal ovaloids are analytic when n is even and are of
exactly C n-1 smoothness when n is odd. This substantially improves the previously …

We present the results of theoretical research of the generalized hypersherical function (HS)
by generalizing two known functions related to the sphere hypersurface and hypervolume …

In this paper, we present the theoretical research results of certain characteristics of the
generalized hyperspherical function with two degrees of freedom as independent …