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  2. Arithmetico-geometric sequence - Wikipedia

    en.wikipedia.org/wiki/Arithmetico-geometric_sequence

    The elements of an arithmetico-geometric sequence () are the products of the elements of an arithmetic progression (in blue) with initial value and common difference , = + (), with the corresponding elements of a geometric progression (in green) with initial value and common ratio , =, so that [4]

  3. Art gallery problem - Wikipedia

    en.wikipedia.org/wiki/Art_gallery_problem

    In decision problem versions of the art gallery problem, one is given as input both a polygon and a number k, and must determine whether the polygon can be guarded with k or fewer guards. This problem is ∃ R {\displaystyle \exists \mathbb {R} } -complete , as is the version where the guards are restricted to the edges of the polygon. [ 10 ]

  4. Archimedes's cattle problem - Wikipedia

    en.wikipedia.org/wiki/Archimedes's_cattle_problem

    Archimedes's cattle problem (or the problema bovinum or problema Archimedis) is a problem in Diophantine analysis, the study of polynomial equations with integer solutions. Attributed to Archimedes , the problem involves computing the number of cattle in a herd of the sun god from a given set of restrictions.

  5. Equation solving - Wikipedia

    en.wikipedia.org/wiki/Equation_solving

    A solution of an equation is often called a root of the equation, particularly but not only for polynomial equations. The set of all solutions of an equation is its solution set. An equation may be solved either numerically or symbolically. Solving an equation numerically means that only numbers are admitted as solutions.

  6. Iterative method - Wikipedia

    en.wikipedia.org/wiki/Iterative_method

    If an equation can be put into the form f(x) = x, and a solution x is an attractive fixed point of the function f, then one may begin with a point x 1 in the basin of attraction of x, and let x n+1 = f(x n) for n ≥ 1, and the sequence {x n} n ≥ 1 will converge to the solution x.

  7. Frobenius solution to the hypergeometric equation - Wikipedia

    en.wikipedia.org/wiki/Frobenius_solution_to_the...

    Since z = 1 − x, the solution of the hypergeometric equation at x = 1 is the same as the solution for this equation at z = 0. But the solution at z = 0 is identical to the solution we obtained for the point x = 0, if we replace each γ by α + β − γ + 1. Hence, to get the solutions, we just make this substitution in the previous results.

  8. At least 5 shows canceled after drones fell from the sky at ...

    www.aol.com/least-5-shows-canceled-drones...

    At least five drone shows have been canceled or have paused the use of the systems, after several drones struck a crowd at a holiday show in Orlando on December 21.

  9. Initial value problem - Wikipedia

    en.wikipedia.org/wiki/Initial_value_problem

    The Banach fixed point theorem is then invoked to show that there exists a unique fixed point, which is the solution of the initial value problem. An older proof of the Picard–Lindelöf theorem constructs a sequence of functions which converge to the solution of the integral equation, and thus, the solution of the initial value problem.