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In mathematics, Euler's identity[ note 1] (also known as Euler's equation) is the equality where. 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 .
In fluid dynamics, the drag equation is a formula used to calculate the force of drag experienced by an object due to movement through a fully enclosing fluid. The equation is: where. is the drag coefficient – a dimensionless coefficient related to the object's geometry and taking into account both skin friction and form drag.
The partial sums of the series 1 + 2 + 3 + 4 + 5 + 6 + ⋯ are 1, 3, 6, 10, 15, etc.The nth partial sum is given by a simple formula: = = (+). This equation was known ...
A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.
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 ...
The first use of an equals sign, equivalent to 14 x + 15 = 71 in modern notation. From The Whetstone of Witte by Robert Recorde of Wales (1557). [ 1] In mathematics, an equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign =. [ 2][ 3] The word equation and its cognates in ...
If equation 1 of Kvålseth [12] is used (this is the equation used most often), R 2 can be less than zero. If equation 2 of Kvålseth is used, R 2 can be greater than one. In all instances where R 2 is used, the predictors are calculated by ordinary least-squares regression: that is, by minimizing SS res .
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.