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The term algebra is derived from the Arabic word al-jabr meaning 'the reunion of broken parts' that he used for naming one of these methods in the title of his main treatise. [31] [32] Algebra became an area in its own right only with François Viète (1540–1603), who introduced the use of variables for representing unknown or unspecified ...
The number π (/ p aɪ / ⓘ; spelled out as "pi") is a mathematical constant, approximately equal to 3.14159, that is the ratio of a circle's circumference to its diameter.It appears in many formulae across mathematics and physics, and some of these formulae are commonly used for defining π, to avoid relying on the definition of the length of a curve.
Of particular note is the use in Chinese mathematics of a decimal positional notation system, the so-called "rod numerals" in which distinct ciphers were used for numbers between 1 and 10, and additional ciphers for powers of ten. [106]
An equivalent definition of entropy is the expected value of the self-information of a variable. [ 1 ] Two bits of entropy: In the case of two fair coin tosses, the information entropy in bits is the base-2 logarithm of the number of possible outcomes — with two coins there are four possible outcomes, and two bits of entropy.
The history of scientific method considers changes in the methodology of scientific inquiry, not the history of science itself. The development of rules for scientific reasoning has not been straightforward; scientific method has been the subject of intense and recurring debate throughout the history of science, and eminent natural philosophers and scientists have argued for the primacy of ...
A dot, rather than a blank, was first seen to denote zero, in a decimal system, in the Bakhshali manuscript. [171] The usage of the zero in the Bakhshali manuscript was dated from between 3rd and 4th centuries, making it the earliest known usage of a written zero, in a decimal place value system. [172]
The Iranian and Indo-Aryan branches separated quite early. It is the Indo-Aryan branch that moved into eastern Iran and then south into South Asia in the first half of the 2nd millennium BCE. Once in ancient India, the Indo-Aryan language underwent rapid linguistic change and morphed into the Vedic Sanskrit language. [66]