-
between this
horocycle and the
radii is 1. The
ratio of the arc
lengths between two
radii of two
concentric horocycles where the
horocycles are a distance...
-
ideal point, the
centre of the
horocycle).
Through every pair of
points there are two
horocycles. The
centres of the
horocycles are the
ideal points of the...
-
there are 4
distinct types of
generalized circles or cycles: circles,
horocycles, hypercycles, and
geodesics (or "hyperbolic lines"). In the Poincaré disk...
-
boundary circle are not distorted. All
other circles are distorted, as are
horocycles and
hypercycles Chords that meet on the
boundary circle are
limiting parallel...
-
circles can be
interpreted as
horocycles. In
hyperbolic geometry any two
horocycles are congruent. When
these horocycles are cir****scribed by apeirogons...
- to some
given horocycle.
These numbers are the
hyperbolic distance x h {\displaystyle x_{h}} from P {\displaystyle P} to the
horocycle, and the (signed)...
- arcs of
horocycles. The
choice of log 2 {\displaystyle \log 2} as the
distance between the two
horocycles causes one of the two arcs of
horocycles (the...
- of the
sphere it
projects generalized circles (geodesics, hypercycles,
horocycles, and circles) in the
hyperbolic plane to
generalized circles (lines or...
-
covering map is
periodic in the x
direction of
period 2π, and
takes the
horocycles y = c to the
meridians of the
pseudosphere and the
vertical geodesics...
-
terms horosphere and
horocycle are due to Lobachevsky, who
established various results showing that the
geometry of
horocycles and the
horosphere in...
