Triangle center Since rotations and translations may be regarded as double reflections they too must preserve triangle centers. These invariance properties provide justification for the definition. Some other names for dilation are uniform scaling, isotropic scaling, homothety, and homothecy. The study of triangle centers traditionally is concerned with Euclidean geometry, but triangle centers can also be studied in hyperbolic geometry. Using gyrotrigonometry, expressions for trigonometric barycentric coordinates can be calculated that have the same form for both Euclidean and hyperbolic geometry. In order for the expressions to coincide, the expressions must "not" encapsulate the specification of the angle sum being 180 degrees.
Degrees of freedom (statistics) degrees of freedom. In some complicated settings, such as unbalanced split-plot designs, the sums-of-squares no longer have scaled chi-squared distributions. Comparison of sum-of-squares with degrees-of-freedom is no longer meaningful, and software may report certain fractional 'degrees of freedom' in these cases. Such numbers have no genuine degrees-of-freedom interpretation, but are simply providing an "approximate" chi-squared distribution for the corresponding sum-of-squares. The details of such approximations are beyond the scope of this page. Several commonly encountered statistical distributions (Student's t, Chi-Squared, F) have parameters that are commonly referred to as "degrees of freedom". This terminology simply reflects that in many applications