Hyperbolic Geometry and the Hillam–Thron Theorem
نویسندگان
چکیده
منابع مشابه
Hyperbolic geometry and the Hillam-Thron theorem
Every open ball within R∞ has an associated hyperbolic metric and Möbius transformations act as hyperbolic isometries from one ball to another. The Hillam-Thron Theorem is concerned with images of balls under Möbius transformation, yet existing proofs of the theorem do not make use of hyperbolic geometry. We exploit hyperbolic geometry in proving a generalisation of the Hillam-Thron Theorem and...
متن کاملHyperbolic Geometry, Nehari’s Theorem, Electric Circuits, and Analog Signal Processing
Underlying many of the current mathematical opportunities in digital signal processing are unsolved analog signal processing problems. For instance, digital signals for communication or sensing must map into an analog format for transmission through a physical layer. In this layer we meet a canonical example of analog signal processing: the electrical engineer’s impedance matching problem. Impe...
متن کاملThe Hyperbolic Menelaus Theorem in The Poincaré Disc Model of Hyperbolic Geometry
In this note, we present the hyperbolic Menelaus theorem in the Poincaré disc of hyperbolic geometry. 2000 Mathematical Subject Classi cation: 30F45, 20N99, 51B10, 51M10 Keywords and phrases: hyperbolic geometry, hyperbolic triangle, gyrovector 1. Introduction Hyperbolic Geometry appeared in the rst half of the 19 century as an attempt to understand Euclids axiomatic basis of Geometry. It is ...
متن کاملA New Proof of Menelaus’s Theorem of Hyperbolic Quadrilaterals in the Poincaré Model of Hyperbolic Geometry
In this study, we present a proof of the Menelaus theorem for quadrilaterals in hyperbolic geometry, and a proof for the transversal theorem for triangles.
متن کاملTrigonometric Proof of Steiner-lehmus Theorem in Hyperbolic Geometry
In this note, we present a short trigonometric proof to the Steiner Lehmus Theorem in hyperbolic geometry. 2000 Mathematics Subject Classification: 30F45, 20N99, 51B10, 51M10
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Geometriae Dedicata
سال: 2006
ISSN: 0046-5755,1572-9168
DOI: 10.1007/s10711-006-9053-4