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
Venus Equilateral by a low-power source. Powered by batteries, the driver tube enables the multi-G constant-boost spaceships seen throughout the series. At the series opening both Mars and Venus have been colonized. Both are described as having shirt-sleeve environments in at least some regions. Eleven of the thirteen Venus Equilateral stories were published in "Astounding Science Fiction" between 1942 and 1945. They were: Smith wrote a 12th story, "Mad Holiday", for the first book collection "Venus Equilateral" (1947) (which omitted "Lost Art" and "Identity"), and a 13th story, "The External Triangle", for Harry Harrison's 1973 anthology "Astounding". All 13 stories were included