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
Schema for vertical declining dials graphical techniques were used to derive formula_1 and formula_2 and from it formula_3. There are four basic angles that are needed to construct a vertical declining dial, Waugh described them such: The four basic calculation have a certain symmetry. At this point only three lines matter, the vertical, the substyle length and substyle height. A circle marked off in 15° angles is needed (circular protractor). Before the protractor became ubiquitous, compasses and the Scale of Chords were used for laying out an angle. This method originally used them. At this point only three lines matter, the vertical, the substyle length