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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]
The derivative of a constant term is 0, so when a term containing a constant term is differentiated, the constant term vanishes, regardless of its value. Therefore the antiderivative is only determined up to an unknown constant term, which is called "the constant of integration" and added in symbolic form (usually denoted as ). [2]
[1] [2] The terms mathematical constant or physical constant are sometimes used to distinguish this meaning. [3] A function whose value remains unchanged (i.e., a constant function). [4] Such a constant is commonly represented by a variable which does not depend on the main variable(s) in question.
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.
The graph of the constant function y = c is a horizontal line in the plane that passes through the point (0, c). [2] In the context of a polynomial in one variable x, the constant function is called non-zero constant function because it is a polynomial of degree 0, and its general form is f(x) = c, where c is nonzero.
The degree of is 1+1+2=4. The degree of a nonzero constant is 0. For example, the degree of −7 is 0. The degree of a monomial is sometimes called order, mainly in the context of series. It is also called total degree when it is needed to distinguish it from the degree in one of the variables.
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The constant first appeared in a 1734 paper by the Swiss mathematician Leonhard Euler, titled De Progressionibus harmonicis observationes (Eneström Index 43), where he described it as "worthy of serious consideration". [2] [3] Euler initially calculated the constant's value to 6 decimal places. In 1781, he calculated it to 16 decimal places.