# Arcs in hyperbolic geometry¶

AUTHORS:

• Hartmut Monien (2011 - 08)

class sage.plot.hyperbolic_arc.HyperbolicArc(A, B, options)

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

INPUT:

• a, b - coordinates of the hyperbolic arc in the complex plane

• options - dict of valid plot options to pass to constructor

EXAMPLES:

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, alpha=1, fill=False, thickness=1, rgbcolor='blue', zorder=2, linestyle='solid', **options)

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

INPUT:

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

OPTIONS:

• 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.

Examples:

Show a hyperbolic arc from 0 to 1:

sage: hyperbolic_arc(0, 1)
Graphics object consisting of 1 graphics primitive


Show a hyperbolic arc from 1/2 to $$i$$ with a red thick line:

sage: hyperbolic_arc(1/2, I, color='red', thickness=2)
Graphics object consisting of 1 graphics primitive


Show a hyperbolic arc form $$i$$ to $$2 i$$ with dashed line:

sage: hyperbolic_arc(I, 2*I, linestyle='dashed')
Graphics object consisting of 1 graphics primitive
sage: hyperbolic_arc(I, 2*I, linestyle='--')
Graphics object consisting of 1 graphics primitive