Beitrag zur Sphärik
Compact hyperbolic tetrahedra with non-obtuse dihedral angles.
Given a combinatorial description C of a polyhedron having E edges, the space of dihedral angles of all compact hyperbolic polyhedra that realize C is generally not a convex subset of RE. If C has five or more faces, Andreev's Theorem states that the corresponding space of dihedral angles AC obtained by restricting to non-obtuse angles is a convex polytope. In this paper we explain why Andreev did not consider tetrahedra, the only polyhedra having fewer than five faces, by demonstrating that the...
Cylinder and horoball packing in hyperbolic space.
Démonstration du théorème fondamental relatif au pôle et à la polaire dans le cercle
Hyperbolization of Euclidean ornaments.
Hyperideal polyhedra in hyperbolic 3-space
A hyperideal polyhedron is a non-compact polyhedron in the hyperbolic -space which, in the projective model for , is just the intersection of with a projective polyhedron whose vertices are all outside and whose edges all meet . We classify hyperideal polyhedra, up to isometries of , in terms of their combinatorial type and of their dihedral angles.
Intersecting pencil of hyperbolic circles
Krychlový obsah šikmého rovnoběžnostěnu bez užívání sférické trigonometrie
La conjecture des soufflets
On sait depuis les travaux de Bricard et de Connelly qu’il existe dans l’espace euclidien des polyèdres (non convexes) qui sont flexibles : on peut les déformer continûment sans changer la forme de leurs faces. La conjecture des soufflets affirme que le volume interieur de ces polyèdres est constant au cours de la déformation. Elle a été démontrée récemment par I. Sabitov, qui a pour cela utilisé des outils algébriques inattendus dans ce contexte.
Note de trigonométrie élémentaire
Note sur la résolution, au moyen de tableaux graphiques, de certains problèmes de cosmographie et de trigonométrie sphérique
Note sur un problème élémentaire de géométrie sphérique
Odvození základních vzorců sférické trigonometrie pomocí některých pouček determinantních
On the area of a polygon in the hyperbolic plane.
On the existence of triangle with given angle and opposite angle bisectors length.
On the generalized stereographic projection.
On the Non-Euclidian Geometry
On the planarity of the equilateral, isogonal pentagon.
Properties of triangulations obtained by the longest-edge bisection
The Longest-Edge (LE) bisection of a triangle is obtained by joining the midpoint of its longest edge with the opposite vertex. Here two properties of the longest-edge bisection scheme for triangles are proved. For any triangle, the number of distinct triangles (up to similarity) generated by longest-edge bisection is finite. In addition, if LE-bisection is iteratively applied to an initial triangle, then minimum angle of the resulting triangles is greater or equal than a half of the minimum angle...
Representation of curves of constant width in the hyperbolic plane.