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
Lectures of the Three Degrees in Craft Masonry Lectures of the Three Degrees in Craft Masonry The Lectures of the Three Degrees in Craft Masonry is a series of manuals on Freemasonry that are arranged in the form of catechisms to be memorized. They cover rituals and symbolism associated with the three degrees of Craft Freemasonry in question and answer form. During the second half of the 19th century, the Lectures gradually ceased to be used regularly in English Lodges. The question and answer procedure was the traditional way in which Freemasons were instructed in Masonic ritual and symbolism before printed ritual books became more widely available. Usually,