What is the 47th Problem of Euclid, anyway?
Once upon a time (like when our ritual was written about two centuries or so back), everyone studied geometry from the plan laid out by Euclid. Sometimes in the original Greek. The 47th problem or proposition, as Euclid approached the subject matter, was what is more commonly known now as the Pythagorean theorem: If a and b are the sides of a right triangle (the length of the sides, that is), and c is the hypotenuse, then a2 + b2 = c2. There are probably a dozen distinct ways to prove this theorem. The usual lines drawn on a typical Masonic illustration of this Master’s emblem hint at one way. The converse is also true (i.e., if the squares add up the right way, then the triangle is a right triangle). If a, b, and c are integers, the set (a,b,c) is called a Pythagorean triple. There are infinitely many distinct such triples (“distinct” meaning that there is no number larger than 1 which divides all three of the numbers; i.e., 6:8:10 is not considered distinct from 3:4:5). Proof: If N i
