number: The Algebraic and Transcendental Numbers
A real or complex number z is called algebraic if it is the root of a polynomial equation z n + a n − 1 z n − 1 + … + a 1 z + a 0 = 0, where the coefficients a 0, a 1, … a n − 1 are all rational; if z cannot be a root of such an equation, it is said to be transcendental. The number
squaring the circle by straight edge and compass alone (see geometric problems of antiquity ). The number e has also been found to be transcendental, although it still remains unknown whether e + π is transcendental.
- The Real Numbers
- The Integers and Rational Numbers
- The Complex Numbers
- The Algebraic and Transcendental Numbers
- The Natural Numbers
The Columbia Electronic Encyclopedia, 6th ed. Copyright © 2012, Columbia University Press. All rights reserved.
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