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irrational number

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irrational number

Number that cannot be expressed as an exact fraction. Irrational numbers include some square roots (for example, √2, √3, and √5 are irrational); numbers such as π (for circles), which is approximately equal to the decimal 3.14159; and e (the base of natural logarithms, approximately 2.71828). If an irrational number is expressed as a decimal it would go on for ever without repeating. An irrational number multiplied by itself gives a rational number.



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He sets up this story by harkening back to the times of the ancient Greeks and Pythagoreans' attempts to deal with irrational numbers, MIT Pr, 2003, 213 p.
Beginning with natural numbers and covering the realms of infinity from prime numbers to parallel lines, the authors explore how mathematicians have tried to grasp the ungraspable, Profiles of individuals range from Pythagoras, who theorized about irrational numbers, to Georg Cantor, who proved that infinity can come in different sizes.
Since then, this never-ending, never-repeating, irrational number has been called the Golden Number or the Golden Ratio and linked to patterns ranging from the petal arrangement of roses to the composition of the "Mona Lisa.
 
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