Angle trisection drawn through formula_25 to the semicircle, resulting in the intersection formula_28. The angle formula_48 generated by formula_49 and formula_50 is the angle formula_51 sought. Another means to trisect an arbitrary angle by a "small" step outside the Greek framework is via a ruler with two marks a set distance apart. The next construction is originally due to Archimedes, called a "Neusis construction", i.e., that uses tools other than an "un-marked" straightedge. The diagrams we use show this construction for an acute angle, but it indeed works for any angle up to 180 degrees. This requires three facts from geometry (at
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