Lobachevsky’s formula

Let $A B$ be a line. Let $M, T$ be two points so that $M$ not lies on $A B$ , $T$ lies on $A B$ , and $M T$ perpendicular to $A B$ . Let $M D$ be any other line who meets $A T$ in $D$ .In a hyperbolic geometry, as $D$ moves off to infinity along $A T$ the line $M D$ meets the line $M S$ which is said to be parallel to $A T$ . The angle $\widehat{SMT}$ is called the angle of parallelism for perpendicular distance $d$ , and is given by

P(d)=2\tan^{-1}(e^{-d}),

which is called Lobachevsky’s formula.

Title	Lobachevsky’s formula
Canonical name	LobachevskysFormula
Date of creation	2013-03-22 14:05:53
Last modified on	2013-03-22 14:05:53
Owner	vmoraru (1243)
Last modified by	vmoraru (1243)
Numerical id	6
Author	vmoraru (1243)
Entry type	Definition
Classification	msc 51M10
Defines	angle of parallelism