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) if for no other reason than that, all else being equal, the fewer degrees of freedom, the better indices such as χ will be. It has been shown that degrees of freedom can be used by readers of papers that contain SEMs to determine if the authors of those papers are in fact reporting the correct model fit statistics. In the organizational sciences, for example, nearly half of papers published in top journals report degrees of freedom that are inconsistent with the models described in those papers, leaving the reader to wonder which models were actually tested. A common way