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Simplification is the process of replacing a mathematical expression by an equivalent one that is simpler (usually shorter), according to a well-founded ordering. Examples include:
As a general principle this approach had already been demonstrated by the logician Hugh McColl in 1878, [4] [5] [6] was proved by Archie Blake in 1937, [7] [8] [9] [6] and was rediscovered by Edward W. Samson and Burton E. Mills in 1954 [10] [6] and by Raymond J. Nelson in 1955.
In the case of two nested square roots, the following theorem completely solves the problem of denesting. [2]If a and c are rational numbers and c is not the square of a rational number, there are two rational numbers x and y such that + = if and only if is the square of a rational number d.
It is unknown whether these constants are transcendental in general, but Γ( 1 / 3 ) and Γ( 1 / 4 ) were shown to be transcendental by G. V. Chudnovsky. Γ( 1 / 4 ) / 4 √ π has also long been known to be transcendental, and Yuri Nesterenko proved in 1996 that Γ( 1 / 4 ), π, and e π are algebraically independent.
Napier's bones is a manually operated calculating device created by John Napier of Merchiston, Scotland for the calculation of products and quotients of numbers. The method was based on lattice multiplication, and also called rabdology, a word invented by Napier.
Trigonometric identities may help simplify the answer. [ 1 ] [ 2 ] Like other methods of integration by substitution, when evaluating a definite integral, it may be simpler to completely deduce the antiderivative before applying the boundaries of integration.
Simplicity is the state or quality of being simple.Something easy to understand or explain seems simple, in contrast to something complicated. Alternatively, as Herbert A. Simon suggests, something is simple or complex depending on the way we choose to describe it. [1]
In mathematics, like terms are summands in a sum that differ only by a numerical factor. [1] Like terms can be regrouped by adding their coefficients. Typically, in a polynomial expression, like terms are those that contain the same variables to the same powers, possibly with different coefficients.