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
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