Geometry, Volume 2, Issue 3

It was known in antiquity that the sum of the three angles of a triangle equals $\pi$. Surprisingly, it was not until 1952 that the corresponding question for a tetrahedron was addressed. In that year, J.W. Gaddum proved that the sum of the four solid...

In this paper, we first make and discuss a conjecture concerning Newtonian potentials in Euclidean n space which have all their mass on the unit sphere about the origin and are normalized to be one at the origin. The conjecture essentially divides th...

The Napoleon–Barlotti theorem belongs to the family of theorems related to the Petr–Douglas–Neumann theorem. The Napoleon–Barlotti theorem states: On the sides of an affine-regular n-gon construct regular n-gons. Then the cent...

In this paper, we propose a class of elementary plane geometry problems closely related to the title of this paper. Here, a circle is the one-dimensional curve bounding a disk. For any non-negative integer, a circle is called n-enclosing if it contai...

Inversion with respect to a unit sphere is a powerful tool when dealing with many problems in Mathematics. This inversion preserves harmonicity in ${\mathbb{R}}^2,$ but it does not in ${\mathbb{R}}^n,$ for $n>2.$ Lord Kelvin overcame this problem by defining a new (at the time...

In 2014, Paul Yiu constructed two equilateral triangles inscribed in a Kiepert hyperbola associated with a reference triangle. It was asserted that each of the equilateral triangles is triply perspective with the reference triangle, and in each case,...