Irrational Numbers

The ancient Greek mathematicians discovered irrational numbers through the study of geometry and trigonometry. Irrational numbers come from the root function of certain numbers, from trigonometric ratios such as pi or from the limit functions such as the special number e. The word irrational literally means a number that cannot be described as a ratio. So any common fraction of one integer over another is not an irrational number. Irrational numbers in decimal form yields a decimal fraction which has an infinite nonrepeating end to the decimal part. So irrational numbers cannot be completely expressed either as a common fraction or a decimal fraction. They can only be estimated to the nearest decimal point. The set of irrational numbers is infinite and along with the complementary set of rational numbers completes the set of real numbers.

The irrational numbers include pi, phi, the logarithmic value e and the square root of two.

Math Mysteries: Unlike common fractions an irrational number cannot be completely described as a ratio or as a decimal fraction due to its infinitely repeating random decimal. It therefore may never be able to be exactly determined. The best supercomputers can only estimate irrational numbers.