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
Zero degrees of freedom concentrates all probability at zero. All of this leaves open the question of what happens with zero degrees of freedom when the noncentrality parameter is not zero. The noncentral chi-squared distribution with zero degrees of freedom and with noncentrality parameter "μ" is the distribution of This concentrates probability "e" at zero; thus it is a mixture of discrete and continuous distributions Zero degrees of freedom In statistics, the non-central chi-squared distribution with zero degrees of freedom can be used in testing the null hypothesis that a sample is from a uniform distribution on the interval (0, 1). This distribution was