We claim that F [subset] [h.sup.-1] (U) for some isometry h of the hyperbolic plane [H.sup.2] = D.
of the isometry group Iso([H.sup.2]) of the hyperbolic plane [H.sup.2] = D.
In the diagram, AB is a "line" in the
hyperbolic plane, that is, a circle orthogonal to the circumference of the shaded disk which represents the
hyperbolic plane.
With Dynamic Geometry, students can experience working in the hyperbolic plane and sphere, and explore the properties of the non-Euclidean geometries.
Tessellations of the Euclidean, elliptic, and hyperbolic plane for Mathematica 4.0.
By (61), we know that a is a
hyperbolic plane curve; that is, [[tau].sub.h] = 0.
The
hyperbolic plane, however, lies outside of daily experience of the physical world.
Weeks of Canton, N.Y., suggests making "hyperbolic paper" from a large number of equilateral triangles as one way to get a feel for the
hyperbolic plane.
New to this expanded second edition is Daina Taimina discussion of her own adventures with the
hyperbolic planes as well as the experiences of some of her readers.
London, March 26 (ANI): 'Crocheting Adventures with
Hyperbolic Planes' has won the Diagram Prize, which rewards the oddest book title of the year.
Escher skillfully convey the illusion of infinitely repeating forms and the strange properties of
hyperbolic planes. Other artists have dabbed in representations of four-dimensional forms.