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The geometric series a + ar + ar 2 + ar 3 + ... is an infinite series defined by just two parameters: coefficient a and common ratio r. Common ratio r is the ratio of any term with the previous term in the series. Or equivalently, common ratio r is the term multiplier used to calculate the next term in the series. The following table shows ...
Principal symbol. The variation formula computations above define the principal symbol of the mapping which sends a pseudo-Riemannian metric to its Riemann tensor, Ricci tensor, or scalar curvature. The principal symbol of the map assigns to each a map from the space of symmetric (0,2)-tensors on to the space of (0,4)-tensors on given by.
In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here ), and is denoted by the symbol . Given two linearly independent vectors a and b, the cross product, a × b ...
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 ...
Heron's formula. In geometry, Heron's formula (or Hero's formula) gives the area of a triangle in terms of the three side lengths Letting be the semiperimeter of the triangle, the area is [1] It is named after first-century engineer Heron of Alexandria (or Hero) who proved it in his work Metrica, though it was probably known centuries earlier.
Geometry index. In coordination chemistry and crystallography, the geometry index or structural parameter ( τ) is a number ranging from 0 to 1 that indicates what the geometry of the coordination center is. The first such parameter for 5-coordinate compounds was developed in 1984. [1] Later, parameters for 4-coordinate compounds were developed.
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.
The geometric distribution is the discrete probability distribution that describes when the first success in an infinite sequence of independent and identically distributed Bernoulli trials occurs. Its probability mass function is where is the number of trials and is the probability of success in each trial.
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