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The same 1 / μ = 3 + √ 8 (the silver ratio squared) also is observed in the unfolded general continued fractions of both the natural logarithm of 2 and the n th root of 2 (which works for any integer n > 1) if calculated using 2 = 1 + 1.
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
Calculus. In mathematics, the harmonic series is the infinite series formed by summing all positive unit fractions: The first terms of the series sum to approximately , where is the natural logarithm and is the Euler–Mascheroni constant. Because the logarithm has arbitrarily large values, the harmonic series does not have a finite limit: it ...
In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator. [1]
A simple fraction (also known as a common fraction or vulgar fraction, where vulgar is Latin for "common") is a rational number written as a / b or , where a and b are both integers. [9] As with other fractions, the denominator (b) cannot be zero. Examples include 1 2 , − 8 5 , −8 5 , and 8 −5 .
In mathematics, the Leibniz formula for π, named after Gottfried Wilhelm Leibniz, states that = + + = = +,. an alternating series.. It is sometimes called the Madhava–Leibniz series as it was first discovered by the Indian mathematician Madhava of Sangamagrama or his followers in the 14th–15th century (see Madhava series), [1] and was later independently rediscovered by James Gregory in ...
One half is one of the few fractions which are commonly expressed in natural languages by suppletion rather than regular derivation. In English, for example, compare the compound "one half" with other regular formations like "one-sixth". A half can also be said to be one part of something divided into two equal parts.
The square root of 2 is equal to the length of the hypotenuse of a right-angled triangle with legs of length 1. The square root of 2, often known as root 2 or Pythagoras' constant, and written as √ 2, is the unique positive real number that, when multiplied by itself, gives the number 2. It is more precisely called the principal square root ...
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