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.
The length of a unitary transformation for characteristic 2.
The Mathieu group and its pseudogroup extension .
The maximum size of a partial spread in is .
The minimum rank problem over finite fields.
The minimum size of complete caps in .
The Missing Seventh Circle.
The Möbius-Pompeiu metric property.
The n -Point Condition and Rough CAT(0)
We show that for n ≥ 5, a length space (X; d) satisfies a rough n-point condition if and only if it is rough CAT(0). As a consequence, we show that the class of rough CAT(0) spaces is closed under reasonably general limit processes such as pointed and unpointed Gromov-Hausdorff limits and ultralimits.
The Neuberg cubic in locus problems.
The nine points circle and Euler's line. (El círculo de los nueve puntos y la recta de Euler.)
The nonexistence of certain projective planes of order 15.