Divisible tilings in the hyperbolic plane.
Broughton, S.Allen, Haney, Dawn M., McKeough, Lori T., Smith Mayfield, Brandy (2000)
The New York Journal of Mathematics [electronic only]
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Displaying similar documents to “Properties of triangulations obtained by the longest-edge bisection”
Divisible tilings in the hyperbolic plane.
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The Electronic Journal of Combinatorics [electronic only]
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Andreev’s Theorem on hyperbolic polyhedra
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In 1970, E.M.Andreev published a classification of all three-dimensional compact hyperbolic polyhedra (other than tetrahedra) having non-obtuse dihedral angles. Given a combinatorial description of a polyhedron, , Andreev’s Theorem provides five classes of linear inequalities, depending on , for the dihedral angles, which are necessary and sufficient conditions for the existence of a hyperbolic polyhedron realizing with the assigned dihedral angles. Andreev’s Theorem also shows that...
The envelope of the Wallace-Simpson lines of a triangle. A simple proof of the Steiner problem on the deltoid.
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A simple proof is presented of a famous, and difficult, theorem by Jakob Steiner. By means of a straightforward transformation of the triangle, the proof of the theorem is reduced to the case of the equilateral triangle. Several relations of the Steiner deltoid with the Feuerbach circle and the Morley triangle appear then as obvious.
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Bonk, Mario, Cherry, William (1999)
Annales Academiae Scientiarum Fennicae. Mathematica
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