Theband model is aconformalmodel of thehyperbolic 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${\displaystyle |dz|\sec (\mathrm{Im}z)}$.

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 arehypercycles whose common axis is the line through the middle of the band.

• Mercator projection

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• Conformal Models of the Hyperbolic Geometry

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