Hyperbolic geometry model

Details Hyperbolic geometry model Hyperbolic geometry model

1977-10-26

1980-01-15

Grieb, William H.

G09B 2304

Patent

active

041831535

ABSTRACT:
A hyperbolic geometry model formed by several pieces of flexible material joined along their edges in a predetermined manner. In one embodiment, the pieces are polygons arranged so that the sum of the angles about each vertex or corner exceeds 360.degree.. In a second embodiment the pieces are elongated strips joined edge-to-edge about a center line with the inner strips being comparatively straight and the strips away from the center line having a progressively decreasing radius of curvature. In a final embodiment the pieces are arcuate strips joined edge-to-edge about a center point with the radius of curvature of the strips progressively increasing to a finite limit away from the center point. The resulting hyperbolic geometry model is a sheet of flexible material which, because of its increasing fullness away from the center of the model, exhibits geometric properties which illustrate the characteristics of a hyperbolic plane.

REFERENCES:
patent: 800721 (1905-10-01), Coolidge
patent: 1880130 (1932-09-01), Goldbach
patent: 2682118 (1954-06-01), Larsen
patent: 3614835 (1971-10-01), Rice et al.
"Repeating Designs in Surfaces of Negative Curvature"; Article in American Mathematical Monthly; Jan. 1937, pp. 33-35.

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