Integer triangle cosine equals 0, ±1/2, or ±1. The only ones of these giving an angle strictly between 0° and 180° are the cosine value 1/2 with the angle 60°, the cosine value –1/2 with the angle 120°, and the cosine value 0 with the angle 90°. The only combination of three of these, allowing multiple use of any of them and summing to 180°, is three 60° angles. Conditions are known in terms of elliptic curves for an integer triangle to have an integer ratio "N" of the circumradius to the inradius. The smallest case, that of the equilateral triangle, has
Three degrees of influence three-degrees-of-influence property. And additional analytic approaches to observational data have also been supportive, including matched sample estimation, and reshuffling techniques (validating the edge directionality test proposed by Christakis and Fowler in their 2007 paper as an identification strategy). The three degrees of influence property has also been noted, by other groups, using observational data regarding criminal networks. Christakis and Fowler reviewed critical and supportive findings regarding the three degrees of influence phenomenon and the analytic approaches used to discern it in 2013. In addition, subsequent studies (by many research groups, including Christakis and Fowler) have found strong causal evidence of