Hyperbolic geometry or hypercycle, then the triangle has no circumscribed circle. As in spherical and elliptical geometry, in hyperbolic geometry if two triangles are similar, they must be congruent. A special polygon in hyperbolic geometry is the regular apeirogon, a uniform polygon with an infinite number of sides. In Euclidean geometry, the only way to construct such a polygon is to make the side lengths tend to zero and the apeirogon is indistinguishable from a circle, or make the interior angles tend to 180 degrees and the apeirogon approaches a straight line. However, in hyperbolic geometry, a regular apeirogon has sides of
Six Degrees: The Science of a Connected Age Six Degrees: The Science of a Connected Age Six Degrees: The Science of a Connected Age (2004 in paperback, and 2003 in hardcover, ) is a popular science book by Duncan J. Watts covering the application of network theory to sociology. The book covers Watts' own work on small-world networks, and continues on to cover scale-free networks, network searching, epidemics and network failures, social decision making, thresholds in networks, and innovation in large organizations and its lack. In addition to covering the theoretical models and empirical case studies, the book also includes several stories about the character of the researchers