Olympic triangle be perfectly sharp, either, since it is a course. Traditionally the configuration of the triangle is an equilateral triangle (3 equal sides and 3 equal angles of 60 degrees) with a ratio of the windward leg to a reaching leg being 1:1. In that case the course length for the 9 legs described above is 9 times the length of the windward leg. The angle at each point of the triangle is 60 degrees. The windward leg is generally aligned with the average wind direction. Another configuration is a triangle with a right angle at the wing mark and 45
Sum of angles of a triangle The relation between angular defect and the triangle's area was first proven by Johann Heinrich Lambert. One can easily see how hyperbolic geometry breaks Playfair's axiom, Proclus' axiom (the parallelism, defined as non-intersection, is intransitive in an hyperbolic plane), the equidistance postulate (the points on one side of, and equidistant from, a given line do not form a line), and Pythagoras' theorem. A circle cannot have arbitrarily small curvature, so the three points property also fails. The sum of the angles can be arbitrarily small (but positive). For an ideal triangle, a generalization of hyperbolic triangles, this sum is equal