# Triangles in hyperbolic geometry¶

AUTHORS:

• Hartmut Monien (2011 - 08)
class sage.plot.hyperbolic_triangle.HyperbolicTriangle(A, B, C, options)

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

INPUT:

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

EXAMPLES:

Note that constructions should use hyperbolic_triangle:

sage: from sage.plot.hyperbolic_triangle import HyperbolicTriangle
sage: print HyperbolicTriangle(0, 1/2, I, {})
Hyperbolic triangle (0.000000000000000, 0.500000000000000, 1.00000000000000*I)

sage.plot.hyperbolic_triangle.hyperbolic_triangle(a, b, c, rgbcolor='blue', thickness=1, zorder=2, alpha=1, linestyle='solid', fill=False, **options)

Return a hyperbolic triangle in the complex hyperbolic plane with points (a, b, c). Type ?hyperbolic_triangle to see all options.

INPUT:

• a, b, c - complex numbers in the upper half complex plane

OPTIONS:

• alpha - default: 1
• fill - default: False
• 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 triangle with coordinates 0, $$1/2+i\sqrt{3}/2$$ and $$-1/2+i\sqrt{3}/2$$:

sage: hyperbolic_triangle(0, -1/2+I*sqrt(3)/2, 1/2+I*sqrt(3)/2)


A hyperbolic triangle with coordinates 0, 1 and 2+i and a dashed line:

sage: hyperbolic_triangle(0, 1, 2+i, fill=true, rgbcolor='red', linestyle='--')


#### Previous topic

Arcs in hyperbolic geometry