Spherical geometry other geometric concepts are defined as in plane geometry, but with straight lines replaced by great circles. Thus, in spherical geometry, angles are defined between great circles, resulting in a spherical trigonometry that differs from ordinary trigonometry in many respects; for example, the sum of the interior angles of a triangle exceeds 180 degrees. Spherical geometry is "not" elliptic geometry, but is rather a "subset" of elliptic geometry. For example, it shares with that geometry the property that a line has no parallels through a given point. Contrast this with Euclidean geometry, in which a line has one parallel through
Degrees of freedom (statistics) other distributions that arise in associated statistical testing problems. While introductory textbooks may introduce degrees of freedom as distribution parameters or through hypothesis testing, it is the underlying geometry that defines degrees of freedom, and is critical to a proper understanding of the concept. Although the basic concept of degrees of freedom was recognized as early as 1821 in the work of astronomer and mathematician Carl Friedrich Gauss, its modern definition and usage was first elaborated by English statistician William Sealy Gosset in his 1908 "Biometrika" article "The Probable Error of a Mean", published under the pen name "Student". While