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? The practical lesson to be drawn from the argument is not to use words like "there" in a loose, unscientific way, without specifying whether you mean "located there" or "occupying space there." In the humoristic magazine "Annals of Improbable Research", Anders Sandberg has presented a calculation based on theories of information physics and quantum gravity, establishing an upper bound of 8.6766×10 angels. Comparing medieval superstition and modern science, George Bernard Shaw wrote in the introduction to the play "Saint Joan" that "The medieval doctors of divinity who did not pretend to settle how many angels could dance on the point