# hyperbolic plane

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Related to hyperbolic plane: hyperbolic geometry

## hyperbolic plane

[¦hī·pər‚bäl·ik ′plān]
(mathematics)
A two-dimensional vector space E on which there is a nondegenerate, symmetric or alternating form ƒ(x,y) such that there exists a nonzero element w in E for which ƒ(w,w) = 0.
References in periodicals archive ?
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.
In contrast to the rigid body, H is a cylindrical paraboloid, rather than an ellipsoid and M, instead of the sphere, changes its type according to the geometric setting: it is a cylinder, in the Euclidcan case; a sphere, in the elliptic case, and a hyperboloid, of either one, or two sheets, or a double cone in the case of the hyperbolic plane. The intersection of the energy paraboloid with these surfaces accounts for all the geometric types of the solutions.
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.

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