- In
hyperbolic geometry, a
horosphere (or parasphere) is a
specific hypersurface in
hyperbolic n-space. It is the
boundary of a horoball, the
limit of a...
-
number of faces. Each cell is a
hexagonal tiling whose vertices lie on a
horosphere, a
surface in
hyperbolic space that
approaches a
single ideal point at...
- the Böröczky
bound is
approximately 85.327613%, and is
realized by the
horosphere ****ng of the order-6
tetrahedral honeycomb with Schläfli
symbol {3,3...
-
limit at a
single ideal point.
These Euclidean tilings are
inscribed in a
horosphere just as
polyhedra are
inscribed in a
sphere (which
contains zero ideal...
- away from each
other and stay at an
infinite distance off its centre. A
horosphere is the 3-dimensional
version of a horocycle. In
Euclidean space, all curves...
-
space is a
complete simply connected space with
nonpositive curvature.
Horosphere a
level set of
Busemann function.
Injectivity radius The
injectivity radius...
- {\displaystyle {\overline {\mathbf {p} \mathbf {q} }}} . Let H be some
horosphere such that
points of the form ( w , x , 0 , … , 0 ) {\displaystyle (w,x...
-
Mathematics 180 (2014), 137–196.
Arxiv with Hee Oh:
Apollonian ****ngs and
Horospheres on
Hyperbolic 3-manifolds. J. Amer. Math. Soc. 24 (2011), 603–648. Arxiv...
- if
Euclidean geometry was. (The
reverse implication follows from the
horosphere model of
Euclidean geometry.) In the
hyperbolic model,
within a two-dimensional...
-
Beltrami also
showed that n-dimensional
Euclidean geometry is
realized on a
horosphere of the (n + 1)-dimensional
hyperbolic space, so the
logical relation between...
