The Square Root Murder

The question was quite simple: How long a fence you need to divide diagonally a one mile square plot into two equal triangles? This geometrical problem was posed some 2500 years ago. When Hippasus of Metapontum heard it, he rolled up his shirt's sleeves and soon he figured out the answer. Using the Pythagorean Theorem, he found that the length of the fence corresponded to the square root of 2. He could not calculate the exact length which was somewhere between one and two miles. Thus, Hippasos discovered an irrational number that defied being expressed as the ratio of integers. The Pythagoreans were shocked. The discovery emerged as a cardinal heresy that shattered the foundations of their mathematical mysticism, the worship and devotion to whole numbers and their ratios, a world ruled by reason and harmony, The Pythagorean Brotherhood was a fanatical religious cult and its members tried to conceal the discovery of the irrational numbers. According to ancient stories, they were so outraged by the disclosure of the square root of two that during a boat trip his fellow mathematicians tossed Hippassos into the sea.