New interpolation inequalities to Euler's R >= 2r - Dorin Andrica and Dan Stefan Marinescu The purpose of this paper is to obtain some...
Gergonne meets Sangaku - Paris Pamfilos In this article we discuss the relation of some hyperbolas, naturally associated with the Gergonne point...
Side lengths of Morley triangles and tetrahedra - Dragutin Svrtan and Darko Veljan The famous Morley theorem says that the adjacent angle...
Another purely synthetic proof of Lemoine's theorem - Nguyen Tien Dung In this article, we give another purely synthetic proof the Lemoine's...
Convexity and non-differentiable singularities in Mortici's paper on Fermat-Torricelli points - Martin Celli We give two proofs of Mortici's...
Equilateral Jacobi triangles - Glenn T. Vickers Given any triangle and any three angles (α, β, γ), the Jacobi construction produces a triangle...
An improved inequality for the perimeter of a quadrilateral - Elliott A. Weinstein and John D. Klemm We demonstrate that a new inequality for the...
A simple synthetic proof of Lemoine's theorem - Tran Quang Hung Using similar triangles and cyclic quadrilaterals, we shall give a simple...
Pascal's hexagram and the geometry of the Ricochet configuration - Jaydeep Chipalkatti This paper is a study of a geometric arrangement called...
Putting the icosahedron into the octahedron - Paris Pamfilos We compute the dimensions of a regular tetragonal pyramid, which allows a cut by a...
Steiner-Lehmus type results related to the Gergonne point of a triangle - Mark Shattuck A Gergonne cevian (abbreviated GC) is a line segment...
Another simple construction of the golden section with equilateral triangles - Tran Quang Hung A simple construction of the golden section with...
Do dogs know the bifurcation locus - Li Zhou A dog runs at speed r and swims at speed s, with r > s. For a fixed point A in a lake with a...
Chains of tangent circles inscribed in a triangle - Giovanni Lucca Starting from the incircle of a generic triangle, we construct three infinite...
Counting the number of isosceles triangles in rectangular regular grids - Chai Wah Wu In general graph theory, the only relationship between...
Circle chains inscribed in symmetrical lunes and integer sequences - Giovanni Lucca We derive the conditions for inscribing, inside a symmetrical...
The golden ratio and regular polygons - Manfred Pietsch We give a simple construction of a chord of the circumcircle of an isosceles triangle...
A toroidal approach to the Archimedean quadrature - Gera T. Soldatos An "Archimedean'' quadrature is attempted ``borrowing" π from the...
A note on conic sections and tangent circles - Jan Kristian Haugland This article presents a result on circles tangent to a given conic section...
Iterated harmonic divisions and the golden ratio - Frank Leitenberger On the projective real line we consider sequences of points in which every...
