Hyperbolic perpendicular line
The construction of hyperbolic perpendicular lines. As usual this is done via the intersection of two circles.
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Raoul @ Koalatux
Hyperbolic Geometry
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Hyperbolic midpoint
Construction of a hyperbolic midpoint. This works the same as in the euclidean case.
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Angle bisection
Construction of a angle bisecting line. This works the same as in the euclidean case.
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Center of circle
The classical construction for finding the center point of a circle.
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Theorem of Thales
The theorem of Thales does not hold in the hyperbolic plane.
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Circumcircle of a hyperbolic triangle
The constructoin of a circumcircle does in principle work, but sometimes the the lines do not intersect thus the midpoint can not be found.
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Incircle of a hyperbolic triangle
Construction of an incircle of an hyperbolic triangle works like in the euclidean case.
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Golden ratio
The usual construction of the golden ratio fails. Mathematically, there exists a golden ratio, but it can not be costructed this way.
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Mirror circle
Mirroring a circle again and again along a line ...
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Hyperbolic regular pentagon
Two similar constructions of hyperbolic regular pentagons. Both constructions fail, as the diagonals can not be constructed by means of the golden ratio as it is done in the euclidean case.
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Hyperbolic regular hexagon
The classical construction of an hyperbolic hexagon fails too. The well known formula U = 2*pi*r for circles has to be modified for hyperbolic circles to U = 2*pi*sinh(r).
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