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# Triangles in hyperbolic geometry

AUTHORS:

- Hartmut Monien (2011 - 08)

class `sage.plot.hyperbolic_triangle.``HyperbolicTriangle`(A, B, C, options)

  Bases: `sage.plot.bezier_path.BezierPath`

  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)
      Graphics object consisting of 1 graphics primitive

  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='--')
      Graphics object consisting of 1 graphics primitive

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