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
Incidence (geometry) Incidence (geometry) In geometry, an incidence relation is a heterogeneous relation that captures the idea being expressed when phrases such as "a point "lies on" a line" or "a line is "contained in" a plane" are used. The most basic incidence relation is that between a point, , and a line, , sometimes denoted . If the pair is called a "flag". There are many expressions used in common language to describe incidence (for example, a line "passes through" a point, a point "lies in" a plane, etc.) but the term "incidence" is preferred because it does not have the