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
Attentat (novel) absorption of a societal concept which has not yet been refuted? Some minor oversights are present in this work. One example is where the author writes, "the square of my hypotenuse was equal to the sum of my right angles," whereas the square of the hypotenuse should be equal to the sum of the squares of the two other sides. In another quote, "it was six o'clock in the morning in Japan therefore 2pm at Ethel's" is erroneous even if it is not specified whether she lives in France or Belgium We do know however that the location is in