Ptolemy's table of chords to the arc angle in degrees as is to 3, or more precisely, the ratio can be made as close as desired to ≈ by making "θ" small enough. Thus, for the arc of °, the chord length is slightly more than the arc angle in degrees. As the arc increases, the ratio of the chord to the arc decreases. When the arc reaches 60°, the chord length is exactly equal to the number of degrees in the arc, i.e. chord 60° = 60. For arcs of more than 60°, the chord is less than the arc, until an arc
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