quadratic irrational number (also known as a quadratic irrational or quadratic surd) is an irrational number that is the solution to some quadratic equation...

of a non-zero polynomial, namely bx − a. Quadratic irrational numbers, irrational solutions of a quadratic polynomial ax2 + bx + c with integer coefficients...

root of 2 was likely the first number proved irrational. The golden ratio is another famous quadratic irrational number. The square roots of all natural...

gives the roots of the quadratic equation, but the solutions are expressed in a form that often involves a quadratic irrational number, which is an algebraic...

In algebraic number theory, a quadratic field is an algebraic number field of degree two over Q {\displaystyle \mathbf {Q} } , the rational numbers. Every...

{\displaystyle SL(2,\mathbb {Z} ).} A quadratic irrational number is an irrational real root of the quadratic equation a x 2 + b x + c = 0 {\displaystyle...

square is irrational. For other proofs that the square root of any non-square natural number is irrational, see Quadratic irrational number or Infinite...

Quadratic field, an algebraic number field of degree two over the field of rational numbers Quadratic irrational or "quadratic surd", an irrational number...

subset of the algebraic numbers, including the quadratic irrationals and other forms of algebraic irrationals. Applying any non-constant single-variable algebraic...

theorem Irrational number Square root of two Quadratic irrational Integer square root Algebraic number Pisot–Vijayaraghavan number Salem number Transcendental...

apotome can be interpreted as a quadratic irrational number formed by subtracting one square root of a rational number from another. This concept of the...

In number theory, a Heegner number (as termed by Conway and Guy) is a square-free positive integer d such that the imaginary quadratic field Q [ − d ]...

In number theory, quadratic integers are a generalization of the usual integers to quadratic fields. Quadratic integers are algebraic integers of degree...

Shujā ibn Aslam (c. 850–930) was the first to accept irrational numbers as solutions to quadratic equations, or as coefficients in an equation (often in...

{\displaystyle \varphi } satisfies the quadratic equation φ 2 = φ + 1 {\displaystyle \varphi ^{2}=\varphi +1} and is an irrational number with a value of φ = 1 + 5...

that the simplest kind of number fields (viz., quadratic fields) were already studied by Gauss, as the discussion of quadratic forms in Disquisitiones arithmeticae...

more closely approximated by rational numbers than any algebraic irrational number can be. In 1844, Joseph Liouville showed that all Liouville numbers...

principle of the number field sieve (both special and general) can be understood as an improvement to the simpler rational sieve or quadratic sieve. When using...

real-valued function of an integer or natural number variable). Examples of quadratic growth include: Any quadratic polynomial. Certain integer sequences such...

case that every real number is rational. A real number that is not rational is called irrational. A famous irrational real number is the π, the ratio of...

In mathematics, a quadratic equation (from Latin quadratus 'square') is an equation that can be rearranged in standard form as a x 2 + b x + c = 0 , {\displaystyle...

Quadratic voting is a collective decision-making procedure which involves individuals allocating votes to express the degree of their preferences, rather...

also proves that e is not a root of a quadratic polynomial with rational coefficients; in particular, e2 is irrational. The most well-known proof is Joseph...

also picks out quadratic irrational numbers since ?(x) is rational if and only if x is either rational or a quadratic irrational number, and moreover x...

elementary algebra, completing the square is a technique for converting a quadratic polynomial of the form a x 2 + b x + c {\displaystyle ax^{2}+bx+c} to...

number that can be represented as a ratio of two perfect squares. (See square root of 2 for proofs that this is an irrational number, and quadratic irrational...

(linguistics). The irrational numbers are a set of numbers that includes all real numbers that are not rational numbers. The irrational numbers are categorised...

quadratic polynomial is a polynomial of degree two in one or more variables. A quadratic function is the polynomial function defined by a quadratic polynomial...

is a quadratic irrational number in the upper half plane then j(τ) is an algebraic integer. In addition he proved that if τ is an algebraic number but...

quadratic irrationals that are PV numbers are: Pisot–Vijayaraghavan numbers can be used to generate almost integers: the nth power of a Pisot number approaches...