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...
39 KB (5,252 words) - 23:37, 2 June 2024
mathematics, a quadratic irrational number (also known as a quadratic irrational or quadratic surd) is an irrational number that is the solution to some...
11 KB (1,627 words) - 22:45, 17 March 2024
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 −...
53 KB (6,843 words) - 10:11, 5 June 2024
Pi (redirect from Ludolph transcendental number)
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...
145 KB (17,361 words) - 16:26, 10 June 2024
more closely approximated by rational numbers than any algebraic irrational number can be. In 1844, Joseph Liouville showed that all Liouville numbers...
34 KB (5,030 words) - 13:48, 13 May 2024
the root of a non-zero polynomial, namely bx − a. Quadratic irrational numbers, irrational solutions of a quadratic polynomial ax2 + bx + c with integer...
13 KB (1,502 words) - 16:38, 20 April 2024
Irrationality is cognition, thinking, talking, or acting without rationality. Irrationality often has a negative connotation, as thinking and actions...
4 KB (376 words) - 22:19, 13 February 2024
Ratio (section Irrational ratios)
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)...
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on a Diophantine approximation. The theorem states that for every irrational number ξ there are infinitely many relatively prime integers m, n such that...
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Diophantine approximation (redirect from Metrical number theory)
approximations of any irrational number. The constant in this result may not be further improved without excluding some irrational numbers (see below)....
30 KB (4,058 words) - 14:28, 2 May 2024