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Euler's identity. In mathematics, Euler's identity [note 1] (also known as Euler's equation) is the equality. is pi, the ratio of the circumference of a circle to its diameter. Euler's identity is named after the Swiss mathematician Leonhard Euler. It is a special case of Euler's formula when evaluated for .
Mathematical fallacy. In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept called mathematical fallacy. There is a distinction between a simple mistake and a mathematical fallacy in a proof, in that a mistake in a proof leads to an invalid proof while in the best-known ...
The imaginary unit or unit imaginary number ( i) is a solution to the quadratic equation x2 + 1 = 0. Although there is no real number with this property, i can be used to extend the real numbers to what are called complex numbers, using addition and multiplication. A simple example of the use of i in a complex number is 2 + 3i.
Moreover, the slogan "two plus two equals five", is the title of the collection of absurdist short stories Deux et deux font cinq (Two and Two Make Five, 1895), by Alphonse Allais; and the title of the imagist art manifesto 2 x 2 = 5 (1920), by the poet Vadim Shershenevich.
Less-than sign. The less-than sign is a mathematical symbol that denotes an inequality between two values. The widely adopted form of two equal-length strokes connecting in an acute angle at the left, <, has been found in documents dated as far back as the 1560s. In mathematical writing, the less-than sign is typically placed between two values ...
A well-known equality featuring the equal sign. The equals sign ( British English) or equal sign ( American English ), also known as the equality sign, is the mathematical symbol =, which is used to indicate equality in some well-defined sense. [1] In an equation, it is placed between two expressions that have the same value, or for which one ...
Difference of two squares. In mathematics, the difference of two squares is a squared (multiplied by itself) number subtracted from another squared number. Every difference of squares may be factored according to the identity. in elementary algebra .
In these formulae, n i − 1 is the number of degrees of freedom for each group, and the total sample size minus two (that is, n 1 + n 2 − 2) is the total number of degrees of freedom, which is used in significance testing. Equal or unequal sample sizes, unequal variances (s X 1 > 2s X 2 or s X 2 > 2s X 1