Irrational number

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In mathematics, the irrational numbers are all the real numbers that are not rational numbers; that is, irrational numbers are those that cannot be expressed as the ratio of two integers. Geometrically, when the ratio of lengths of two line segments is an irrational number, the line segments are also described as being incommensurable, meaning that they share no "measure" in common; that is, there is no length ("the measure"), no matter how short, that could be used to express the lengths of both of the two given segments as integer multiples of itself. Among irrational numbers are the ratio π of a circle's circumference to its diameter, Euler's number e, the golden ratio φ, and the square root of two. In fact, all square roots of natural numbers, other than of perfect squares, are irrational. Like any real number, an irrational number can be expressed in positional notation; however, it does not terminate or end with a repeating sequence. For example, the decimal representation of π starts...

Read on Wikipedia · Image derivative work: Pbroks13 (talk) Square root of 2 triangle.png: en:User:Fredrik Simplified drawing: Rubber Duck (☮ • ✍), Public domain