Hyperbolic Non-Euclidean World
Ch.19 Area Density (Sector) 
We saw a disc model character from the view point of length (cf. Ch.2, Ch.14). Here let us see it from the view point of area.
Look at [Fig 19-1] right. White spots are scattered at regular interval. All spot size is the same. There is no other pattern rather than this if you scatter for regular interval (cf.Ch.10). The farther you go, the smaller spots become to your eyes. That is to say, on a model disc a hyperbolic area occupied by a certain visual area gets bigger when it goes far from the origin. You may call it area density.
[Fig 19-3] shows area density with spray that is equally sprayed in the Hyperbolic NonEuclidean World. Let us call such spray hyperbolic spray. Compare it with that of Poincare's Upper Half Plane (cf. Ch.21). How can we homogenize the spray to see real surface of the Hyperbolic NonEuclidean World? (cf. Ch.20).
Next: Ch.20. Pseudo-sphere 1
Prev: Ch.18 Infinity 3 and Analytic Curve (Lambert's Quadrangle, Projective Plane)
Table of Contents Index