1. Each question required the "controlling spirits" to make a mathematical assumption before answering. For the first, the question of the non-parallel lines, the assumption concerned whether or not they were on the same plane. If they were, they would necessarily meet. If they were not, the correct answer would be no. For the second, the question of determining the circumference of a circle, the assumption concerned the exactitude of the answer required. The formula is: circumference = diameter X pi (22/7). Pi is a transcendental number whose exact value has never been determined. In fact, there are ongoing projects, involving super computers, still seeking the value of pi. So, while every "schoolboy" would know how to find the circumference of a circle, the answer is exact only on those occasions when the diameter is a multiple of 7. Apparently, the spirits did realize that pi was a transcendental number. The offer to produce a formula for "squaring the circle" amounted to an offer to develop the exact value of pi in thirty days.