1 in 60 rule has 90 miles to his next waypoint. He is thus two miles to the left of that and thus the waypoint is 4/3 of a degree (2 × 60/90) to the right, or approximately 1° right. The pilot then adds these two to get 5° and flies 5° right of t his previous heading. One can also use the 1 in 60 rule to approximate distance from a VOR, by flying 90 degrees to a radial and timing how long it takes to fly 10 degrees (the limit of the course deviation indicator). The time in seconds divided by 10
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