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The integral of secant cubed is a frequent and challenging [1] indefinite integral of elementary calculus : where is the inverse Gudermannian function, the integral of the secant function . There are a number of reasons why this particular antiderivative is worthy of special attention: The technique used for reducing integrals of higher odd ...
The space diagonal of the unit cube is √ 3. Distances between vertices of a double unit cube are square roots of the first six natural numbers, including the square root of 3 (√7 is not possible due to Legendre's three-square theorem) This projection of the Bilinski dodecahedron is a rhombus with diagonal ratio √ 3.
Roots of unity can be defined in any field. If the characteristic of the field is zero, the roots are complex numbers that are also algebraic integers. For fields with a positive characteristic, the roots belong to a finite field, and, conversely, every nonzero element of a finite field is a root of unity.
As the volume of a cube is the third power of its sides , third powers are called cubes, by analogy with squares and second powers. A cube has the largest volume among cuboids (rectangular boxes) with a given surface area. Also, a cube has the largest volume among cuboids with the same total linear size (length+width+height).
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 ...
The computation of an n th root is a root extraction. For example, 3 is a square root of 9, since 3 2 = 9, and −3 is also a square root of 9, since (−3) 2 = 9. Any non-zero number considered as a complex number has n different complex n th roots, including the real ones (at most two). The n th root of 0 is zero for all positive integers n ...
The Cube Root of Uncertainty is a collection of science fiction short stories by American writer Robert Silverberg, published in hardcover by Macmillan in 1970 and issued in paperback by Collier Books in 1971. No further editions have been issued. Contents "Introduction" "Passengers" (Orbit 4 1968) "Double Dare" (Galaxy 1956)
Prime power. In mathematics, a prime power is a positive integer which is a positive integer power of a single prime number . For example: 7 = 71, 9 = 32 and 64 = 26 are prime powers, while 6 = 2 × 3, 12 = 22 × 3 and 36 = 62 = 22 × 32 are not. The sequence of prime powers begins: