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
How many angels can dance on the head of a pin? Suite Part II: Let It Grow", a song from the 1973 Grateful Dead album Wake of the Flood, includes the line "As well to count the angels dancing on a pin." In the comic book "The Crow" by James O'Barr, the main character asks this question to one of his victims before killing them, answering himself, "Depends on the tune". The song "Velodrome" from Minnesota rapper Dessa's 2018 album Chime, references this question in the first verse asking, "Aquinas, call on me/ How many angels on the/ Head of your pin?" How many angels can dance on the head of