Triangle sum to more than 180°. A hyperbolic triangle can be obtained by drawing on a negatively curved surface, such as a saddle surface, and a spherical triangle can be obtained by drawing on a positively curved surface such as a sphere. Thus, if one draws a giant triangle on the surface of the Earth, one will find that the sum of the measures of its angles is greater than 180°; in fact it will be between 180° and 540°. In particular it is possible to draw a triangle on a sphere such that the measure of each of its internal
Degrees of freedom (statistics) vector (made up of "n" − 1 degrees of freedom within each of the populations). In statistical testing problems, one usually isn't interested in the component vectors themselves, but rather in their squared lengths, or Sum of Squares. The degrees of freedom associated with a sum-of-squares is the degrees-of-freedom of the corresponding component vectors. The three-population example above is an example of one-way Analysis of Variance. The model, or treatment, sum-of-squares is the squared length of the second vector, with 2 degrees of freedom. The residual, or error, sum-of-squares is with 3("n"−1) degrees of freedom. Of course, introductory books on