Arcs in hyperbolic geometry


  • Hartmut Monien (2011 - 08)
class sage.plot.hyperbolic_arc.HyperbolicArc(A, B, options)

Bases: sage.plot.bezier_path.BezierPath

Primitive class for hyberbolic arc type. See hyperbolic_arc? for information about plotting a hyperbolic arc in the complex plane.


  • a, b - coordinates of the hyperbolic arc in the complex plane
  • options - dict of valid plot options to pass to constructor


Note that constructions should use hyperbolic_arc:

sage: from sage.plot.hyperbolic_arc import HyperbolicArc

sage: print HyperbolicArc(0, 1/2+I*sqrt(3)/2, {})
Hyperbolic arc (0.000000000000000, 0.500000000000000 + 0.866025403784439*I)
sage.plot.hyperbolic_arc.hyperbolic_arc(a, b, rgbcolor='blue', thickness=1, zorder=2, alpha=1, linestyle='solid', fill=False, **options)

Plot an arc from a to b in hyperbolic geometry in the complex upper half plane.


  • a, b - complex numbers in the upper half complex plane connected bye the arc


  • alpha - default: 1
  • thickness - default: 1
  • rgbcolor - default: ‘blue’
  • linestyle - (default: 'solid') The style of the line, which is one of 'dashed', 'dotted', 'solid', 'dashdot', or '--', ':', '-', '-.', respectively.


Show a hyperbolic arc from 0 to 1:

sage: hyperbolic_arc(0, 1)

Show a hyperbolic arc from 1/2 to \(i\) with a red thick line:

sage: hyperbolic_arc(1/2, I, color='red', thickness=2)

Show a hyperbolic arc form \(i\) to \(2 i\) with dashed line:

sage: hyperbolic_arc(I, 2*I, linestyle='dashed')
sage: hyperbolic_arc(I, 2*I, linestyle='--')

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