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Halley's method. In numerical analysis, Halley's method is a root-finding algorithm used for functions of one real variable with a continuous second derivative. Edmond Halley was an English mathematician and astronomer who introduced the method now called by his name. The algorithm is second in the class of Householder's methods, after Newton's ...
Muhamed (horse) Muhamed was a German horse reportedly able to mentally extract the cube roots of numbers, which he would then tap out with his hooves. Raised in the town of Elberfeld by Karl Krall in the late 19th and early 20th centuries, he was one of several supposedly gifted horses, the others being Kluge Hans, Zarif, Amassis, and later ...
Sometimes the term "unit cube" refers in specific to the set [0, 1] n of all n-tuples of numbers in the interval [0, 1]. The length of the longest diagonal of a unit hypercube of n dimensions is , the square root of n and the (Euclidean) length of the vector (1,1,1,....1,1) in n-dimensional space. See also
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 ( musical interval) of a semitone ( Play ⓘ) in twelve-tone equal temperament. This number was proposed for the first time in relationship to ...
where (k=1, 2, 3) is a cube root of 1 (=, = +, and =, where i is the imaginary unit). Here if the radicands under the cube roots are non-real, the cube roots expressed by radicals are defined to be any pair of complex conjugate cube roots, while if they are real these cube roots are defined to be the real cube roots.
The edge length of a cube with total surface area of 1 is or the reciprocal square root of 6. The edge lengths of a regular tetrahedron ( t ), a regular octahedron ( o ), and a cube ( c ) of equal total surface areas satisfy t ⋅ o c 2 = 6 {\displaystyle {\frac {t\cdot o}{c^{2}}}={\sqrt {6}}} .
He illustrates that F and Φ obey the formulas F ∝ 1 / R^2 sinh^2(r/R) and Φ ∝ coth(r/R), where R and r represent the curvature radius and the distance from the focal point, respectively. The concept of the dimensionality of space, first proposed by Immanuel Kant, is an ongoing topic of debate in relation to the inverse-square law.
The square root of a positive integer is the product of the roots of its prime factors, because the square root of a product is the product of the square roots of the factors. Since p 2 k = p k , {\textstyle {\sqrt {p^{2k}}}=p^{k},} only roots of those primes having an odd power in the factorization are necessary.