Hyperbolic geometry: The first 150 years

Hyperbolic Geometry : the First 150 Years

This will be a description of a few highlights in the early history of non-euclidean geometry, and a few miscellaneous recent developments. An Appendix describes some explicit formulas concerning volume in hyperbolic 3-space. The mathematical literature on non-euclidean geometry begins in 1829 with publications by N. Lobachevsky in an obscure Russian journal. The infant subject grew very rapidl...

Universal Hyperbolic Geometry III: First Steps in Projective Triangle Geometry

We initiate a triangle geometry in the projective metrical setting, based on the purely algebraic approach of universal geometry, and yielding in particular a new form of hyperbolic triangle geometry. There are three main strands: the Orthocenter, Incenter and Circumcenter hierarchies, with the last two dual. Formulas using ortholinear coordinates are a main objective. Prominent are five partic...

Neandertals...150 years later.

The place of Neandertals in modern human emergence has been a subject of debate since the first recognized Neandertal skeleton was discovered in 1856. This paper presents an overview of morphological, archaeological, and genetic evidence commonly used in discussions of Neandertals and their evolutionary significance. A brief historical sketch of the argument provides insight into the changing v...

Hyperbolic Geometry

Mendel, 150 years on.

Mendel's paper 'Versuche über Pflanzen-Hybriden' is the best known in a series of studies published in the late 18th and 19th centuries that built our understanding of the mechanism of inheritance. Mendel investigated the segregation of seven gene characters of pea (Pisum sativum), of which four have been identified. Here, we review what is known about the molecular nature of these genes, which...