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From Wikipedia, the free encyclopedia

In geometry, the **band model** is a conformal model of the hyperbolic plane. The band model employs a portion of the Euclidean plane between two parallel lines.^{[1]} Distance is preserved along one line through the middle of the band. Assuming the band is given by , the metric is given by .

Geodesics include the line along the middle of the band, and any open line segment perpendicular to boundaries of the band connecting the sides of the band. Every end of a geodesic either meets a boundary of the band at a right angle or is asymptotic to the midline; the midline itself is the only geodesic that does not meet a boundary.^{[2]} Lines parallel to the boundaries of the band within the band are hypercycles whose centers are the line through the middle of the band.

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