Heptagonal triangle heptagonal triangle's orthic triangle, with vertices at the feet of the altitudes, is similar to the heptagonal triangle, with similarity ratio 1:2. The heptagonal triangle is the only obtuse triangle that is similar to its orthic triangle (the equilateral triangle being the only acute one). The various trigonometric identities associated with the heptagonal triangle include these:, The cubic equation has solutions formula_66 and formula_67 which are the squared sines of the angles of the triangle. The positive solution of the cubic equation equals formula_69 which is twice the cosine of one of the triangle’s angles. We also have: For an
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