Winter Hexagon of one another by following various lines traced through various stars in Orion. The stars in the hexagon are parts of six constellations. Counter-clockwise around the hexagon, starting with Rigel, these are Orion, Taurus, Auriga, Gemini, Canis Minor, and Canis Major. Winter Hexagon The Winter Hexagon or Winter Circle/Oval is an asterism appearing to be in the form of a hexagon with vertices at Rigel, Aldebaran, Capella, Pollux, Procyon, and Sirius. It is mostly upon the Northern Hemisphere's celestial sphere. On most locations on Earth (except the South Island of New Zealand and the south of Chile and Argentina and
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