Hyperbolic triangle the third angle. The triangle where two vertices are ideal points and the remaining angle is right, one of the first hyperbolic triangles (1818) described by Ferdinand Karl Schweikart. The triangle where all vertices are ideal points, an ideal triangle is the largest possible triangle in hyperbolic geometry because of the zero sum of the angles. The relations among the angles and sides are analogous to those of spherical trigonometry; the length scale for both spherical geometry and hyperbolic geometry can for example be defined as the length of a side of an equilateral triangle with fixed angles. The length
Three degrees of influence affect our friends' friends, and so on. However, across a broad set of empirical settings, using both observational and experimental methods, they observed that the effect seems, in many cases, to no longer be meaningful at a social horizon of three degrees. Christakis and Fowler examined phenomena from various domains, such as obesity, happiness, cooperation, and voting. Investigations by other groups have subsequently explored many other phenomena in this way (including crime, social learning, etc.). Influence dissipates after three degrees (to and from friends’ friends’ friends) for three reasons, Christakis and Fowler propose: Initial studies using observational data by Christakis