Saccheri–Legendre theorem Saccheri–Legendre theorem In absolute geometry, the Saccheri–Legendre theorem states that the sum of the angles in a triangle is at most 180°. Absolute geometry is the geometry obtained from assuming all the axioms that lead to Euclidean geometry with the exception of the axiom that is equivalent to the parallel postulate of Euclid. The theorem is named after Giovanni Girolamo Saccheri and Adrien-Marie Legendre. The existence of at least one triangle with angle sum of 180 degrees in absolute geometry implies Euclid's parallel postulate. Similarly, the existence of at least one triangle with angle sum of less than 180 degrees
Decimal degrees radius of the semi-major axis of the Earth at the equator is 6,378,137.0 meters resulting in a circumference of 40,075,161.2 meters. The equator is divided into 360 degrees of longitude, so each degree at the equator represents 111,319.9 meters or approximately 111.32 km. As one moves away from the equator towards a pole, however, one degree of longitude is multiplied by the cosine of the latitude, decreasing the distance, approaching zero at the pole. The number of decimal places required for a particular precision at the equator is: A value in decimal degrees to a precision of 4 decimal places