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In the following Diophantine equations, w, x, y, and z are the unknowns and the other letters are given constants: a x + b y = c {\displaystyle ax+by=c} This is a linear Diophantine equation or Bézout's identity. w 3 + x 3 = y 3 + z 3 {\displaystyle w^ {3}+x^ {3}=y^ {3}+z^ {3}} The smallest nontrivial solution in positive integers is 123 + 13 ...
The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [2] It is called the shoelace formula because of the constant cross-multiplying for the coordinates making up the ...
Quadratic formula. The roots of the quadratic function y = 1 2 x2 − 3x + 5 2 are the places where the graph intersects the x -axis, the values x = 1 and x = 5. They can be found via the quadratic formula. In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation.
Vieta's formulas can equivalently be written as for k = 1, 2, ..., n (the indices ik are sorted in increasing order to ensure each product of k roots is used exactly once). The left-hand sides of Vieta's formulas are the elementary symmetric polynomials of the roots. Vieta's system (*) can be solved by Newton's method through an explicit simple ...
Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. Originally called infinitesimal calculus or "the calculus of infinitesimals ", it has two major branches, differential calculus and integral calculus.
Formula editor. A formula editor is a computer program that is used to typeset mathematical formulas and mathematical expressions. Formula editors typically serve two purposes: They allow word processing and publication of technical content either for print publication, or to generate raster images for web pages or screen presentations.
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Mason's gain formula. Mason's gain formula (MGF) is a method for finding the transfer function of a linear signal-flow graph (SFG). The formula was derived by Samuel Jefferson Mason, [1] for whom it is named. MGF is an alternate method to finding the transfer function algebraically by labeling each signal, writing down the equation for how that ...