Parallels Between Parallels

Abstract

The earth's sun introduces a symmetry in the perception of its trajectory in the sky that naturally partitions the earth's surface into zones of affine and hyperbolic geometry. The affine zones, with single geometric parallels, are located north and south of the geographic tropical parallels. The hyperbolic zone, with multiple geometric parallels, is located between the geographic parallels. Evidence of this geometric partition is suggested in the geographic environment--in the design of houses and of gameboards.