# Category: Algebraic numbers

Twelfth root of two
The twelfth root of two or (or equivalently ) is an algebraic irrational number, approximately equal to 1.0594631. It is most important in Western music theory, where it represents the frequency ratio
Hard hexagon model
In statistical mechanics, the hard hexagon model is a 2-dimensional lattice model of a gas, where particles are allowed to be on the vertices of a triangular lattice but no two particles may be adjace
Geometric Constructions
Geometric Constructions is a mathematics textbook on constructible numbers, and more generally on using abstract algebra to model the sets of points that can be created through certain types of geomet
Principal root of unity
In mathematics, a principal n-th root of unity (where n is a positive integer) of a ring is an element satisfying the equations In an integral domain, every primitive n-th root of unity is also a prin
Algebraic number
An algebraic number is a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients. For example, the golden ratio, , is an algebraic number,
Root of unity
In mathematics, a root of unity, occasionally called a de Moivre number, is any complex number that yields 1 when raised to some positive integer power n. Roots of unity are used in many branches of m
Roth's theorem
In mathematics, Roth's theorem is a fundamental result in diophantine approximation to algebraic numbers. It is of a qualitative type, stating that algebraic numbers cannot have many rational number a
Imaginary unit
The imaginary unit or unit imaginary number (i) is a solution to the quadratic equation . Although there is no real number with this property, i can be used to extend the real numbers to what are call
Salem number
In mathematics, a Salem number is a real algebraic integer α > 1 whose conjugate roots all have absolute value no greater than 1, and at least one of which has absolute value exactly 1. Salem numbers
Fundamental theorem of ideal theory in number fields
In number theory, the fundamental theorem of ideal theory in number fields states that every nonzero proper ideal in the ring of integers of a number field admits unique factorization into a product o
Pisot–Vijayaraghavan number
In mathematics, a Pisot–Vijayaraghavan number, also called simply a Pisot number or a PV number, is a real algebraic integer greater than 1, all of whose Galois conjugates are less than 1 in absolute
Chebyshev nodes
In numerical analysis, Chebyshev nodes are specific real algebraic numbers, namely the roots of the Chebyshev polynomials of the first kind. They are often used as nodes in polynomial interpolation be
Gaussian integer
In number theory, a Gaussian integer is a complex number whose real and imaginary parts are both integers. The Gaussian integers, with ordinary addition and multiplication of complex numbers, form an
Perron number
In mathematics, a Perron number is an algebraic integer α which is real and exceeds 1, but such that its conjugate elements are all less than α in absolute value. For example, the larger of the two ro
Cube root of two
No description available.
Look-and-say sequence
In mathematics, the look-and-say sequence is the sequence of integers beginning as follows: 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, 31131211131221, ... (sequence in the OEIS). To genera
Eisenstein integer
In mathematics, the Eisenstein integers (named after Gotthold Eisenstein), occasionally also known as Eulerian integers (after Leonhard Euler), are the complex numbers of the form where a and b are in
Algebraic integer
In algebraic number theory, an algebraic integer is a complex number which is integral over the integers. That is, an algebraic integer is a complex root of some monic polynomial (a polynomial whose l
Constructible number
In geometry and algebra, a real number is constructible if and only if, given a line segment of unit length, a line segment of length can be constructed with compass and straightedge in a finite numbe