The Square Root of Two

The Square Root of Two

The square root of two, also known as Pythagoras & apos;s constant, is the positive real number that, when multiplied by itself, gives the number 2. Geometrically the square root of two is the length of a diagonal across a square with sides of one unit of length; this follows from the Pythagorean theorem. It was probably the first number known to be irrational. Its numerical value truncated to five decimal places is: 1.41421.

In mathematics, an irrational number is any real number that is not a rational number; that is, it is a number which cannot be expressed as a fraction x/y, where x and y are integers, with y being non-zero. Basically, this means numbers that cannot be represented as simple fractions. It can be proven that irrational numbers are precisely those real numbers that cannot be represented as terminating or repeating decimals, although mathematicians do not take that to be the definition.

I do not profess to be a skilled mathematician and will go no further than this brief explanation. I was introduced to the use of the square root of two by an acquaintance in the market, who described the ratio as commonly occurring within musical notes. At first I wasn't quite sure how to use this, until I began to sit down and study wave relationships and noted that two derivations of the number frequently occurred: 41.4% and its “opposite” 58.6%, being 100 - 41.4.