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
Savilian Professor of Geometry world, saying that the professor of geometry should teach Euclid's "Elements", Apollonius's "Conics", and the works of Archimedes; tuition in trigonometry was to be shared by the two professors. As many students would have had little mathematical knowledge, the professors were also permitted to provide instruction in basic mathematics in English (as opposed to Latin, the language used in education at Oxford at the time). Savile's first choice for the professorship of geometry was Edmund Gunter, Professor of Astronomy at Gresham College, London. It was reported that Gunter demonstrated the use of his sector and quadrant, but Savile regarded this