The generalized sine law and some inequalities for simplices.
The generating rank of the symplectic line-Grassmannian.
The Geometric and Dynamic Essence of Phyllotaxis
We present a dynamic geometric model of phyllotaxis based on two postulates, primordia formation and meristem expansion. We find that Fibonacci, Lucas, bijugate and multijugate are all variations of the same unifying phenomenon and that the difference lies in the changes in position of initial primordia. We explore the set of all initial positions and color-code its points depending on the phyllotactic pattern that arises.
The geometrical Barbilian's work from a modern point of view.
The geometry of in translation planes of even order .
The geometry of GL(2,q) in translation planes of even order (Corrigendum).
The geometry of null systems, Jordan algebras and von Staudt's theorem
We characterize an important class of generalized projective geometries by the following essentially equivalent properties: (1) admits a central null-system; (2) admits inner polarities: (3) is associated to a unital Jordan algebra. These geometries, called of the first kind, play in the category of generalized projective geometries a rôle comparable to the one of the projective line in the category of ordinary projective geometries. In this general set-up, we prove an analogue of von Staudt’s...
The Gergonne point generalized through convex coordinates.
The Gromov Invariant of Links.
The group of projectivities in free-like geometries
The Hahn-Banach theorem implies the Banach-Tarski paradox
The hyperbolic Carnot theorem in the Poincaré disc model of hyperbolic geometry.
The hyperbolic triangle centroid
Some gyrocommutative gyrogroups, also known as Bruck loops or K-loops, admit scalar multiplication, turning themselves into gyrovector spaces. The latter, in turn, form the setting for hyperbolic geometry just as vector spaces form the setting for Euclidean geometry. In classical mechanics the centroid of a triangle in velocity space is the velocity of the center of momentum of three massive objects with equal masses located at the triangle vertices. Employing gyrovector space techniques we find...
The hyperplanes of .
The inner-product of iso-taxicab geometry.
The intersection conics of six straight lines.
The lattices and Möbius functions of stable closed subrootsystems and Hyperplane complements for classical Weyl Groups.
The Lehmus inequality.
The length of a lemmiscate.
The length of a unitary transformation.