Triangle see that the Earth's surface is locally flat: If we draw an arbitrarily small triangle in the neighborhood of one point on the Earth's surface, the fraction "f" of the Earth's surface which is enclosed by the triangle will be arbitrarily close to zero. In this case the angle sum formula simplifies to 180°, which we know is what Euclidean geometry tells us for triangles on a flat surface. Rectangles have been the most popular and common geometric form for buildings since the shape is easy to stack and organize; as a standard, it is easy to design furniture and
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