two integers. When the ratio of lengths of two line segments is an irrational number, the line segments are also described as being incommensurable, meaning...

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

numbers. For example, the square root of 2 is an irrational number, but it is not a transcendental number as it is a root of the polynomial equation x2 −...

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

approximately equal to 3.14159. The number π appears in many formulae across mathematics and physics. It is an irrational number, meaning that it cannot be expressed...

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

Irrationality is cognition, thinking, talking, or acting without rationality. Irrationality often has a negative connotation, as thinking and actions...

its diameter, which is called π, and is not just an irrational number, but a transcendental number. Also well known is the golden ratio of two (mostly)...

on a Diophantine approximation. The theorem states that for every irrational number ξ there are infinitely many relatively prime integers m, n such that...

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