Algebraic Number
If 
is a Root of the Polynomial equation
 | (1) |
s are Integers and satisfies no similar equation of degree 
, then is an algebraicnumber of degree 
. If is an algebraic number and 
, then it is called an Algebraic Integer. It is alsotrue that if the 
s in | (2) |
If 
is an algebraic number of degree satisfying the Polynomial
 | (3) |
other algebraic numbers 
, 
, ... called the conjugates of . Furthermore, if satisfies any other algebraic equation, then its conjugates also satisfy the same equation (Conway and Guy 1996).Any number which is not algebraic is said to be Transcendental.
See also Algebraic Integer, Euclidean Number, Hermite-Lindemann Theorem,Radical Integer, Semialgebraic Number, Transcendental Number
References
Conway, J. H. and Guy, R. K. ``Algebraic Numbers.'' In The Book of Numbers. New York: Springer-Verlag, pp. 189-190, 1996. Courant, R. and Robbins, H. ``Algebraic and Transcendental Numbers.'' §2.6 in What is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed. Oxford, England: Oxford University Press, pp. 103-107, 1996. Hancock, H. Foundations of the Theory of Algebraic Numbers. Vol. 1: Introduction to the General Theory. New York: Macmillan, 1931. Hancock, H. Foundations of the Theory of Algebraic Numbers. Vol. 2: The General Theory. New York: Macmillan, 1932. Wagon, S. ``Algebraic Numbers.'' §10.5 in Mathematica in Action. New York: W. H. Freeman, pp. 347-353, 1991.
- Euclidean Metric
- Euclidean Motion
- Euclidean Norm
- Euclidean Number
- Euclidean Plane
- Euclidean Space
- Euclid Number
- Euclid's Axioms
- Euclid's Elements
- Euclid's Fifth Postulate
- Euclid's Postulates
- Euclid's Principle
- Euclid's Theorems
- Eudoxus's Kampyle
- Euler Angles
- Euler-Bernoulli Triangle
- Euler Brick
- Euler Chain
- Euler Characteristic
- Euler Constant
- Euler Curvature Formula
- Euler Differential Equation
- Euler Equation
- Euler Formula
- Euler Four-Square Identity