3 papers
math.NT2024
Circumscribed Circles in Integer Geometry
Oleg Karpenkov, Anna Pratoussevitch, Rebecca Sheppard
Integer geometry on a plane deals with objects whose vertices are points in . The congruence relation is provided by all affine transformations preserving the lattice…
math.GT2024
Farey Bryophylla
Oleg Karpenkov, Anna Pratoussevitch
The construction of the Farey tessellation in the hyperbolic plane starts with a finitely generated group of symmetries of an ideal triangle, i.e. a triangle with all vertices on t…
math.NT2023
Lattice angles of lattice polygons
James Dolan, Oleg Karpenkov
This paper is dedicated to a lattice analog to the classical ``sum of interior angles of a polygon theorem''. In 2008, the first formula expressing conditions on the geometric cont…