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# Topic: Geometric

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 Geometric progression - Wikipedia, the free encyclopedia In mathematics, a geometric progression (also inaccurately known as a geometric series, see below) is a sequence of numbers such that the quotient of any two successive members of the sequence is a constant called the common ratio of the sequence. A non-zero geometric progression shows exponential growth or exponential decay. An infinite geometric series is an infinite series whose successive terms have a common ratio. en.wikipedia.org /wiki/Geometric_progression   (511 words)

 Geometric Sequences A geometric sequence is a sequence in which each successive term is formed by multiplying the same number. In a geometric sequence, the ratio between consecutive terms is constant. The sequence is geometric with a first term of 2 and a common ratio of -4/2 = -2. www.saskschools.ca /curr_content/mathb30/seq_series/les2/notes.htm   (234 words)

 MATHGuide's Geometric Sequences In this section, you will learn how to identify geometric sequences, calculate the nth term of geometric sequences, find the number of terms in an geometric sequence and find the sum of geometric sequences. Sequence C is a little different because it seems that we are dividing; yet to stay consistent with the theme of geometric sequences, we must think in terms of multiplication. It may be necessary to calculate the number of terms in a certain geometric sequence. www.mathguide.com /lessons/SequenceGeometric.html   (1373 words)

 DIMACS Workshop Implementation of Geometric Algorithms   (Site not responding. Last check: 2007-10-21) This difficulty arises in part from the conceptual complexity of geometric algorithms, the proliferation of special cases, the dependence of combinatorial decisions on numerical computation, and frequent theoretical focus on worst-case asymptotic behavior. To be useful, geometric algorithms must be able to repair such data, that is, in some fashion eliminate inconsistencies. Geometric data structures are known that can represent complex structures in any dimension. dimacs.rutgers.edu /Workshops/GeomAlgorithms/announcement.html   (346 words)

 PlanetMath: geometric mean are real numbers, we define their geometric mean as See Also: arithmetic mean, general means inequality, weighted power mean, power mean, arithmetic-geometric-harmonic means inequality, root-mean-square, proof of general means inequality, derivation of zeroth weighted power mean, proof of arithmetic-geometric-harmonic means inequality, derivation of geometric mean as the limit of the power mean, mean This is version 2 of geometric mean, born on 2001-10-20, modified 2001-11-09. planetmath.org /encyclopedia/GeometricMean.html   (87 words)

 Geometric Bingo   (Site not responding. Last check: 2007-10-21) Geometric Bingo Lawrence, Anne Wells Community Academy 4815 W. Ohio Street 942-2580 Chicago, Illinois 60644 378-0376 Objectives: Learners in grades 7-10 will be able to name and identify the names of 20 geometric shapes. Students will derive the properties of various geometric figures as questions are formulated to distinguish the shapes. Conclusion: As students play "Geometric Bingo" they are actively thinking about the commonalities and differences exhibited by the figures and the strategical value of the questions they ask. www.iit.edu /~smile/ma8710.html   (581 words)

 The Geometric Series   (Site not responding. Last check: 2007-10-21) Since we use the geometric series constantly when dealing with Laplace transforms, it's important to be very familiar with it. In general a geometric series is of the form S = 1 + x + x^2 + x^3 + x^4 +... In a sense, Laplace transforms are the same basic "trick", but applied to derivatives instead of powers, as discussed in the main article on Laplace transforms. www.mathpages.com /home/508att1.htm   (95 words)

 On Neighbors in Geometric Permutations (ResearchIndex) We conjecture that the maximum number of neighbors in a set of n pairwise disjoint convex bodies is O(n), and we settle this conjecture for d = 2. Hence we obtain an alternative proof of a linear upper bound on the number of geometric permutations for any nite family of pairwise disjoint convex... 9 Sharp bounds on geometric permutations of pairwise disjoint.. citeseer.ist.psu.edu /sharir01neighbors.html   (342 words)

 Discrete Algebra - Sequences and Series - Geometric Progression   (Site not responding. Last check: 2007-10-21) A geometric progression is a sequence in which each term (after the first) is determined by multiplying the preceding term by a constant. The sum of the first n terms of an geometric progression is calculated as The 6th to 10th terms of this geometric sequence is library.thinkquest.org /10030/11snsgp.htm   (195 words)

 Cambridge University GA Research Group Our group works on applications of geometric algebra in physics, computer science and engineering. Geometric Algebra for Physicists (CUP 2003) is now published. A study of the Dirac equation in a fl hole background produces the first calculations of the bound state spectrum. www.mrao.cam.ac.uk /~clifford   (117 words)

 Creating Geometric "Solids"   (Site not responding. Last check: 2007-10-21) The student will investigate geometric solids, surface area, and volumes through variety of constructions and hands-on activities that will allow them to experience first-hand these concepts. Construct the polyhedron, a geometric solid with different numbers of faces, figure shown page 59 of the xerox copy. Actually, models of solids made with straws and similar materials are called "skeletons" of the geometric solid. coe.west.asu.edu /explorer/shapes/staffdevl/5.teacher.instructions.html   (788 words)

 [No title] Analytic, geometric, and numerical techniques are used in the setting of differential geometry to solve pure and applied problems in diverse fields which include global geometry, mathematical physics, algebraic geometry, material science, image processing and optimization. These flows are characterized by the deformation of geometric objects such as metrics, mappings, and submanifolds by geometric quantities such as curvature and consist of partial differential equations of parabolic type. The recent theoretical progress on geometric flows, especially on understanding weak solutions and singularities, together with the recent computational progress on geometric flows makes this an opportune time to hold a workshop which will bring together mathematicians working on the theoretical and numerical aspects of geometric flows. www.ipam.ucla.edu /programs/gf2004   (715 words)

 Geometric Modeling and Processing 2000 Geometric Modeling and Processing 2000 (GMP 2000) will be held in Hong Kong on April 10-12, 2000. GMP 2000 is the first in a biennial international conference series on solid modeling, shape representation and geometric computation. Modeling and processing of geometric shape is fundamental to many disciplines, such as computer graphics, computer vision, CAD/CAM, medical imaging and scientific computation. www.csis.hku.hk /gmp2000   (134 words)

 The Geometry Junkyard: Geometric Models This page describes physical objects corresponding to geometric constructions (and methods for creating such objects), particularly polytopes. The Atomium, structure formed for Expo 1958 in the form of nine spheres, representing an iron crystal. Art in the form of geometric tangles of metal and wood rods. www.ics.uci.edu /~eppstein/junkyard/model.html   (899 words)

 NCTM : Illuminations Lessons : Exploring Geometric Solids and Their Properties   (Site not responding. Last check: 2007-10-21) In this interactive geometry investigation students will explore geometric solids and their properties. Use geometric models to solve problems in other areas of mathematics, such as number and measurement. The views expressed or implied, unless otherwise noted, should not be interpreted as official positions of the Council. illuminations.nctm.org /index_o.aspx?id=122   (226 words)

 A Theoretic Model for Linear Geometric ICA - Theis, Jung, Lang (ResearchIndex) Abstract: Geometric algorithms for linear ICA have recently received some attention due to their pictorial description and their relative ease of implementation. The geometric approach to ICA has been proposed first by Puntonet and Prieto [1] [2] in order to separate linear mixtures. We will reconsider geometric ICA in a solid theoretic framework showing that fixpoints of geometric ICA fulfill a so called geometric convergence condition, which the mixed images of the unit vectors satisfy, too. citeseer.ist.psu.edu /theis01theoretic.html   (570 words)

 Question Corner -- Applications of the Geometric Mean In the same way, the geometric mean is relevant any time several quantities multiply together to produce a product. The geometric mean answers the question, "if all the quantities had the same value, what would that value have to be in order to achieve the same product?" If you calculate this geometric mean you get approximately 1.283, so the average rate of return is about 28% (not 30% which is what the arithmetic mean of 10%, 60%, and 20% would give you). www.math.toronto.edu /mathnet/questionCorner/geomean.html   (2387 words)

 Geometric Harmonic Mean   (Site not responding. Last check: 2007-10-21) In mathematics, the geometric-harmonic mean M(x, y) of two positive real numbers x and y is defined as follows: we first form the geometric mean of x and y and call it g Both of these sequences converge to the same number, which we call the geometric-harmonic mean M(x, y) of x and y. M(x, y) is a number between the geometric and harmonic mean of x and y; in particular it is between x and y. www.wikiverse.org /geometric-harmonic-mean   (141 words)

 Geometric Mean   (Site not responding. Last check: 2007-10-21) The logarithm of the geometric mean is the arithmetic mean of the log transformed data: The geometric mean is an appropriate measure of central tendency when averages of rates or index numbers are required. The geometric mean is calculated from the arithmetic mean of the log transformed data. shazam.econ.ubc.ca /intro/gmean.htm   (195 words)

 Amazon.com: Books: Geometric Modeling   (Site not responding. Last check: 2007-10-21) It integrates the three important functions of geometric modeling: to represent elementary forms (i.e., curves, surfaces, and solids), to shape and assemble these into more complex forms, and to determine concomitant derivative geometric elements (i.e., intersections, offsets, and fillets). Geometric Modeling, Second Edition serves as an invaluable guide to computer graphics and CAD/CAM specialists, applications designers, scientific programmers, teachers, and students. I think everyone who is interested in geometric modeling will find it's beneficial for research as well as for applications. www.amazon.com /exec/obidos/tg/detail/-/0471129577?v=glance   (1163 words)

 Geometric Primitives in Web Design. Introduction - webreference.com Before attempting to tame complex design elements, you must be utterly familiar with simple geometric forms, their uses, misuses, behavior, and limitations. Yes, as little as a century ago you couldn't produce a book without a minimum of rococo decorations (leafs, flowers, tracery, etc.); but these days, a well-balanced composition of simple geometric forms is more likely to qualify as the graphic theme for a book cover or web page. In a sense, rectangles and circles used in design are also sort of "other people's art." A child is unlikely to discover the beauty of ideal circles unless he acquires this notion from the entire design culture surrounding him as he grows up. www.webreference.com /dlab/9707   (572 words)

 Will-Harris House WebFonts/FreeFonts The typeface is Geometric Slabserif 703, which is Bitstream's version of Memphis a typeface designed in 1930 by Rudolph Weiss. They have a simple, geometric shape, and their serifs (the small protrusions from the ends of the letter) are in the "slab" family, which means they, too, are simple. The "x-height" (the height of the lowercase letter "x") is relatively large, but not so large that it makes reading difficult in the web where there is little real control over leading (the space between the lines). www.will-harris.com /fonts/freefonts.htm   (470 words)

 Geometric mean in comparison to arithmetic mean or means calculate - center frequeny calculation average numbers ...   (Site not responding. Last check: 2007-10-21) Geometric mean in comparison to arithmetic mean or means calculate - center frequeny calculation average numbers bandwidth - sengpielaudio Calculation of the geometric mean of two numbers Comparison between the arithmetic mean (average) and the geometric mean. www.sengpielaudio.com /calculator-geommean.htm   (170 words)

 Imaginary Numbers are not Real - the Geometric Algebra of Spacetime   (Site not responding. Last check: 2007-10-21) We show how the definition of a `geometric product' of vectors in 2- and 3-dimensional space provides precise geometrical interpretations of the imaginary numbers often used in conventional methods. Physics is greatly facilitated by the use of Hestenes' spacetime algebra, which automatically incorporates the geometric structure of spacetime. We conclude that geometric algebra is the most powerful and general language available for the development of mathematical physics. www.mrao.cam.ac.uk /~clifford/introduction/intro/intro.html   (192 words)

 Geometric Sculpture of George W. Hart, mathematical sculptor As a sculptor of constructive geometric forms, my work deals with patterns and relationships derived from classical ideals of balance and symmetry. Mathematical yet organic, these abstract forms invite the viewer to partake of the geometric aesthetic. Finally, you might also like to look at some of my 2D computer-generated images, which are concepts for sculptures too difficult to realize physically, or some of my early plotter drawings. www.georgehart.com /sculpture/sculpture.html   (1169 words)

 flipcode - Geometric Algebra Primer Geometric algebra is a new way of dealing with geometrical concepts and relations. Its elegance and ease of use is unparalleled. It turns out that being able to 'calculate' with subspaces is extremely powerful, and solves many of the hacks required by traditional methods. www.flipcode.com /cgi-bin/fcarticles.cgi?show=6134   (156 words)

 Hypergeometric Functions in Exact Geometric Computation (ResearchIndex) A general approach to address nonrobustness in such problems is Exact Geometric Computation (EGC). 6 A new number core for robust numerical and geometric librari.. 4 A Core library for robust numerical and geometric libraries (context) - Karamcheti, Li et al. citeseer.ist.psu.edu /du02hypergeometric.html   (484 words)

 Digital Circuit Sizing via Geometric Programming   (Site not responding. Last check: 2007-10-21) ABSTRACT: This tutorial paper concerns a method for digital circuit sizing based on formulating the problem as a geometric program (GP), a special type of mathematical optimization problem that can be very efficiently solved. We start with a basic gate scaling problem, with delay modeled as a simple RC time constant, and then add various layers of complexity and modeling accuracy, such as accounting for differing fall and rise times, effects of signal transition times, and so on. In all cases our focus is on formulating the problem as a GP, or an extension of GP called generalized geometric programming (GGP). www.stanford.edu /~boyd/gp_digital_ckt.html   (189 words)

 Geometric Abstract Art Encyclopedia Article, Definition, History, Biography   (Site not responding. Last check: 2007-10-21) Find geometric abstract art - Your relevant result is a click away! Geometric abstract art is a form of abstract art based on the use of simple geometric forms placed in nonillusionistic space and combined into nonobjective compositions. Artists who created geometric abstract works include Piet Mondriaan, Victor Vasarely, Kazimir Malevich and Gordon Walters. encyclopedia.localcolorart.com /encyclopedia/Geometric_abstract_art   (247 words)

 Geometric Calculus R & D Home Page Geometric Calculus is a mathematical language for expressing and elaborating geometric concepts. Geometric Calculus provides a rich language for the construction and analysis of mathematical models. This site is devoted primarily to the development of Geometric Calculus with many applications to modeling in physics, mostly the work of David Hestenes. modelingnts.la.asu.edu /GC_R&D.html   (285 words)

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