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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.
This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums. Here, is taken to have the value
It is available free of charge for non-commercial users. [6] License: open source under GPL license (free of charge) Languages: 55; Geometry: points, lines, all conic sections, vectors, parametric curves, locus lines; Algebra: direct input of inequalities, implicit polynomials, linear and quadratic equations; calculations with numbers, points ...
Davenport–Schinzel sequences are named after Harold Davenport and Andrzej Schinzel, who applied them to certain problems in the theory of differential equations. [1] They are finite sequences of symbols from a given alphabet, constrained by forbidding pairs of symbols from appearing in alternation more than a given number of times (regardless of what other symbols might separate them).
Pages for logged out editors learn more. Contributions; Talk; Geometric sequence
Figurate numbers were a concern of the Pythagorean worldview. It was well understood that some numbers could have many figurations, e.g. 36 is a both a square and a triangle and also various rectangles. The modern study of figurate numbers goes back to Pierre de Fermat, specifically the Fermat polygonal number theorem.
The geometric mean of two positive numbers is never greater than the arithmetic mean. [3] So the geometric means are an increasing sequence g 0 ≤ g 1 ≤ g 2 ≤ ...; the arithmetic means are a decreasing sequence a 0 ≥ a 1 ≥ a 2 ≥ ...; and g n ≤ M(x, y) ≤ a n for any n. These are strict inequalities if x ≠ y.
The Geometer's Sketchpad is a commercial interactive geometry software program for exploring Euclidean geometry, algebra, calculus, and other areas of mathematics.It was created as part of the NSF-funded Visual Geometry Project led by Eugene Klotz and Doris Schattschneider from 1986 to 1991 at Swarthmore College. [1]