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A geometric progression, also known as a geometric sequence, is a mathematical sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed number called the common ratio. For example, the sequence 2, 6, 18, 54, ... is a geometric progression with a common ratio of 3.
The geometric series is an infinite series derived from a special type of sequence called a geometric progression.This means that it is the sum of infinitely many terms of geometric progression: starting from the initial term , and the next one being the initial term multiplied by a constant number known as the common ratio .
JTS Topology Suite (Java Topology Suite) is an open-source Java software library that provides an object model for Euclidean planar linear geometry together with a set of fundamental geometric functions.
In addition, the book surveys applications of geometric algorithms in such areas as geographic information systems, geometric shortest path and network optimization and mesh generation. Ding-Zhu Du; Frank Hwang (1995). Computing in Euclidean Geometry. Lectures Notes Series on Computing. Vol. 4 (2nd ed.). World Scientific. ISBN 981-02-1876-1.
When every term of a series is a non-negative real number, for instance when the terms are the absolute values of another series of real numbers or complex numbers, the sequence of partial sums is non-decreasing. Therefore a series with non-negative terms converges if and only if the sequence of partial sums is bounded, and so finding a bound ...
JWildfire is a java-based, open-source fractal flame generator. [24] Mandelbrot Fractal is a fractal explorer written in JavaScript. [25] Fractal Grower is software written in Java for generating Lindenmayer Substitution Fractals (L-systems). [26]
An arithmetico-geometric series is a sum of terms that are the elements of an arithmetico-geometric sequence. Arithmetico-geometric sequences and series arise in various applications, such as the computation of expected values in probability theory , especially in Bernoulli processes .
In geometric query problems, commonly known as geometric search problems, the input consists of two parts: the search space part and the query part, which varies over the problem instances. The search space typically needs to be preprocessed, in a way that multiple queries can be answered efficiently. Some fundamental geometric query problems are: