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The book is written for a general audience, unlike a follow-up work published by Knorr, Textual Studies in Ancient and Medieval Geometry (1989), which is aimed at other experts in the close reading of Greek mathematical texts. [1] Nevertheless, reviewer Alan Stenger calls The Ancient Tradition of Geometric Problems "very specialized and ...
For example, the sequence 2, 6, 18, 54, ... is a geometric progression with a common ratio of 3. Similarly 10, 5, 2.5, 1.25, ... is a geometric sequence with a common ratio of 1/2. Examples of a geometric sequence are powers r k of a fixed non-zero number r, such as 2 k and 3 k. The general form of a geometric sequence is
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 .
However, the problem is among the most interesting in the papyrus, as its setup and even method of solution suggests Geometric progression (that is, geometric sequences), elementary understanding of finite series, as well as the St. Ives problem—even Chace cannot help interrupting his own narrative in order to compare problem 79 with the St ...
An infinite series of any rational function of can be reduced to a finite series of polygamma functions, by use of partial fraction decomposition, [8] as explained here. This fact can also be applied to finite series of rational functions, allowing the result to be computed in constant time even when the series contains a large number of terms.
Doubling the cube, also known as the Delian problem, is an ancient [a] [1]: 9 geometric problem. Given the edge of a cube , the problem requires the construction of the edge of a second cube whose volume is double that of the first.
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
This series is called balanced if a 1... a k + 1 = b 1...b k q. This series is called well poised if a 1 q = a 2 b 1 = ... = a k + 1 b k, and very well poised if in addition a 2 = −a 3 = qa 1 1/2. The unilateral basic hypergeometric series is a q-analog of the hypergeometric series since