Definitions for horocycle
horo·cy·cle

WiktionaryRate this definition:0.0 / 0 votes

1. horocyclenoun

   A curve in hyperbolic geometry whose normals all converge asymptotically.

WikipediaRate this definition:0.0 / 0 votes

1. Horocycle

   In hyperbolic geometry, a horocycle (from Greek ὅριον (hórion) 'border', and κύκλος (kúklos) 'circle'), sometimes called an oricycle, oricircle, or limit circle, is a curve whose normal or perpendicular geodesics all converge asymptotically in the same direction. It is the two-dimensional case of a horosphere (or orisphere). The centre of a horocycle is the ideal point where all normal geodesics asymptotically converge. Two horocycles who have the same centre are concentric. Although it appears as if two concentric horocycles cannot have the same length or curvature, in fact any two horocycles are congruent. A horocycle can also be described as the limit of the circles that share a tangent in a given point, as their radii go towards infinity. In Euclidean geometry, such a "circle of infinite radius" would be a straight line, but in hyperbolic geometry it is a horocycle (a curve). From the convex side the horocycle is approximated by hypercycles whose distances from their axis go towards infinity.

WikidataRate this definition:0.0 / 0 votes

1. Horocycle

   In hyperbolic geometry, a horocycle is a curve whose normal geodesics all converge asymptotically. It is the two-dimensional example of a horosphere. A horocycle can also be described as the limit of the circles that share a tangent in a given point, as their radii go towards infinity. In ordinary euclidean geometry, such a "circle of infinite radius" would be a straight line, but in hyperbolic geometry it curves. From the convex side the horocycle is approximated by hypercycles whose distances go towards infinity. In the Poincaré disk model of the hyperbolic plane, the horocycles are represented by circles tangent to the boundary circle. In the Poincaré half-plane model the horocycles are represented by circles tangent to the boundary line, and lines parallel to the boundary line. In the hyperboloid model they are represented by intersections of the hyperboloid with planes whose normal lies in the asymptotic cone.

How to pronounce horocycle?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

   Australian

   Veena

   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

   British

   Fred

   US English

   Tessa

   South African

How to say horocycle in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of horocycle in Chaldean Numerology is: 9

2. Pythagorean Numerology

   The numerical value of horocycle in Pythagorean Numerology is: 5

References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Horocycle
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Horocycle
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=horocycle