Special Cases of Hyperbolic Parallelograms on the Lobachevsky Plane
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A hyperbolic parallelogram is a quadrangle whose opposite sides are asymptotically parallel. A hyperbolic rectangle is a hyperbolic parallelogram whose diagonals are congruent. A hyperbolic square is a hyperbolic parallelogram whose diagonals are perpendicular and congruent. This paper is devoted to the proof of the existence of hyperbolic rectangles and of hyperbolic squares by means of computations in the Beltrami-Cayley-Klein model of hyperbolic geometry.
- Ryazan State Radio Engineering University Russian Federation
- Academy of Law Management of the Federal Penal Service of Russia Russian Federation
hyperbolic plane, hyperbolic rhombus, hyperbolic rectangle, Cayley-Klein model, Hyperbolic and elliptic geometries (general) and generalizations, hyperbolic square, hyperbolic parallelogram
hyperbolic plane, hyperbolic rhombus, hyperbolic rectangle, Cayley-Klein model, Hyperbolic and elliptic geometries (general) and generalizations, hyperbolic square, hyperbolic parallelogram
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