Articles
Hyperbolische 5-Rechtecke
Published:
2003-06-01
https://doi.org/10.5485/TMCS.2003.0007
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Keywords
hyperbolic geometry Klein-model right-angled pentagons (Hyperbolische Geometrie Klein-Modell rechtwinklige 5-Ecke)
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Copyright (c) 2003 H. Zeitler
This work is licensed under a Creative Commons Attribution 4.0 International License.
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H. (2003). Hyperbolische 5-Rechtecke. Teaching Mathematics and Computer Science, 1(1), 111-123. https://doi.org/10.5485/TMCS.2003.0007
Abstract
The main topic of this paper is the investigation of 5-pentagons whose interior angles are all right angles within the hyperbolic geometry (so-called 5-rectangles). Some knowledge of elementary hyperbolic geometry is required.
At first the existence of such a polygon is shown by construction within the Kleinmodel. Then two formulas due to D. M. Y. Sommerville [3] are proved. This means to juggle with trigonometric formulas of hyperbolic geometry.
In the last years a big number of papers concerning hyperbolic geometry was published. This proves that the interest in this nice discipline is growing again.
At first the existence of such a polygon is shown by construction within the Kleinmodel. Then two formulas due to D. M. Y. Sommerville [3] are proved. This means to juggle with trigonometric formulas of hyperbolic geometry.
In the last years a big number of papers concerning hyperbolic geometry was published. This proves that the interest in this nice discipline is growing again.