# Arcs in hyperbolic geometry¶

AUTHORS:

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

Primitive class for hyberbolic 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, 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.

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)


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='--')


Colors

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Triangles in hyperbolic geometry