Hyperbolic Cosines and Sines Theorems for the Triangle Formed by Arcs of Intersecting Semicircles on Euclidean Plane | Zendy

Robert M. Yamaleev | Zendy

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Hyperbolic Cosines and Sines Theorems for the Triangle Formed by Arcs of Intersecting Semicircles on Euclidean Plane

Author(s) -

Robert M. Yamaleev

Publication year - 2013

Publication title -

journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.252

H-Index - 13

eISSN - 2314-4785

pISSN - 2314-4629

DOI - 10.1155/2013/920528

Subject(s) - mathematics , hyperbolic triangle , curvilinear coordinates , euclidean geometry , mathematical proof , bounded function , trigonometric functions , direction cosine , plane (geometry) , exponential function , hyperbolic geometry , non euclidean geometry , sine , mathematical analysis , pure mathematics , geometry , hyperbolic function , hyperbolic manifold , differential geometry

The hyperbolic cosines and sines theorems for the curvilinear triangle bounded by circular arcs of three intersecting circles are formulated and proved by using the general complex calculus. The method is based on a key formula establishing a relationship between exponential function and the cross-ratio. The proofs are carried out on Euclidean plane

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