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
Equipollence (geometry) used a special notation for the equipollence of segments "AB" and "CD": The following passages, translated by Michael J. Crowe, show the anticipation that Bellavitis had of vector concepts: Thus oppositely directed segments are negatives of each other: formula_2 On a great circle of a sphere, two directed circular arcs are equipollent when they agree in direction and arc length. An equivalence class of such arcs is associated with a quaternion versor Equipollence (geometry) In Euclidean geometry, equipollence is a binary relation between directed line segments. A line segment "AB" from point "A" to point "B" has the opposite direction