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Topic: Geometric Progression

	Draw Sizer - Geometric Progression
		With geometric progression, drawer heights increase by a constant multiplicative factor such that the ratio of consecutive drawer heights is the same.
		A geometric progression of drawer heights may be quite similar to an arithmetic progression depending on the choice of sizing parameters.
		For example, this technique could be used to proportion the spacing of stretchers in a table, the stepped front of a sideboard, the arrangement of decorative molding on a chest or armoire, or even the arrangement of patterns in a segmented wood turning.
	www.woodbin.com /calcs/drawsizer_geometric.htm (425 words)

	AllRefer.com - progression (Mathematics) - Encyclopedia
		progression, in mathematics, sequence of quantities, called terms, in which the relationship between consecutive terms is the same.
		An arithmetic series is the indicated sum of an arithmetic progression, and its sum of the first n terms is given by the formula [2a+(n-1)d]n/2; in the above example the arithmetic series is 3+7+11+15+…, and the sum of the first 5 terms, i.e., when n=5, is [2•3+(5-1)4] 5/2=55.
		A harmonic progression is one in which the terms are the reciprocals of the terms of an arithmetic progression; it therefore has the general form 1/a, 1/(a + d), …, 1/[a+(n-1)d].
	reference.allrefer.com /encyclopedia/P/progrsn.html (374 words)

	Geometric Progression
		A geometric progression is a sequence in which each term (except the first term) is derived from the preceding term by the multiplication of a non-zero constant, which is the common ratio.
		A geometric series is formed by the addition of the terms in a geometric progression.
		Sum to first n terms of a G. Geometric mean.
	library.thinkquest.org /C0110248/algebra/apgpgeom.htm (116 words)

	Grade 11 Issue 4/2004 Mathematics Magazine
		An arithmetic progression is a sequence in which each term after the first is formed by adding a fixed amount, called the common difference, to the preceding term.
		A geometric progression is a sequence in which each term after the first is formed by multiplying the preceding term by a fixed number, called the common ratio.
		Thus, to insert k geometric means between two numbers is to form a geometric progression of k+2 terms having the two given numbers as the first and last terms.
	www.mathematicsmagazine.com /4-2004/Gr11_4_2003.htm (598 words)

	Mind Over Mathematics: Higher Arithmetic -- Residues of Powers
		For geometric numbers, however, there is no simple modulus, under which the individual members of any given geometric progression can be made congruent.
		Calculate the least positive residues of the numbers of the geometric progressions based on 2, 3, 4, with respect to 5 as a modulus.
		With respect to modulus 5, the residues of the geometric progressions based on the numbers 2-5 yield the following results: (The Powers are in the first row; the residues resulting from a specific geometric progression are in the rows which follow.
	members.tripod.com /~american_almanac/residue.htm (1229 words)

	Geometric progression - Wikipedia, the free encyclopedia
		Thus the common ratio gives a family of geometric sequences whose starting value is determined by the scale factor.
		Note that the two kinds of progression are related: taking the logarithm of each term in a geometric progression yields an arithmetic one.
		An infinite geometric series is an infinite series whose successive terms have a common ratio.
	en.wikipedia.org /wiki/Geometric_progression (651 words)

	[No title] (Site not responding. Last check: 2007-10-16)
		For example, an arithmetic progression determines a next number by addition and a geometric progression determines a next number by multiplication.
		Typically, the first value in a geometric progression is the base value itself, and the default base value is 2 (1 is a pretty boring geometric expression).
		A Fibonacci progression is an arithmetic progression where each value in the progression is based upon the summation of the two previous values.
	www.cs.ucd.ie /staff/rem/d011/Practical4.doc (726 words)

	Count On (Site not responding. Last check: 2007-10-16)
		With a geometric progression, the spacing of the grid is increased by multiplication and not addition.
		Geometric progressions have one drawback, however, as the size of the grid may become very large - even if the common ratio is quite small.
		Rather than use the geometrical progression to define the measure for the spacing, we can also use the geometrical progression to define the grid using the Cartesian grid directly.
	www.mathsyear2000.org /explorer/gridwarping/geometric-progressions (589 words)

	gladwell dot com - thinking about yawns
		This is an example of what in mathematics is called a geometric progression.
		Epidemics are another example of geometric progression: when a virus spreads through a population, it doubles and doubles again, until it has (figuratively) grown from a single sheet of paper all the way to the sun in fifty steps.
		As human beings we have a hard time with this kind of progression, because the end result--the effect--seems far out of proportion to the cause.
	www.gladwell.com /tippingpoint/tp_excerpt1.html (682 words)

	Geometric Universe
		These volumes are a reiterating geometric fractal, where each element is a step in the geometric progression.
		These geometric energy constructs may be described as: members of a range of periodically developed fractals, as a volumetric alphabet, as a compact three dimensional binary code, and as a vector description of the elements and their potential bonds.
		To provide an approach to geometry that unites the dimensions, the regular geometric figures, and establishes the beginning from which the study of mathematics, chemistry and physics all may begin.
	www.geometricuniverse.com (967 words)

	The MLM File - The MLM Geometric Progression Recruiting Scheme (Site not responding. Last check: 2007-10-16)
		Definition: A geometric progression is a sequence, such as the numbers 1, 3, 9, 27, 81, in which each figure is multiplied by the same factor (in this case 3), in order to obtain the following figure.
		In MLM, the end result of your geometric progression is the SUM of all the figures from all levels (in this case, 121 people to your 4th level).
		Of course, the huge problem for a new distributor is that he or she will never know exactly where they are positioned in the progression, or how large the progression has been in the past, is at the moment, or will be in the future.
	www.themlmfile.com /geopro.htm (707 words)

	All Elementary Mathematics - Study Guide - Algebra - Arithmetic and geometric progressions ...
		The numerical sequence, in which each next term beginning from the second is equal to the previous term, multiplied by the constant for this sequence number q, is called a geometric progression.
		For it the notion of a sum of infinitely decreasing geometric progression is determined as a number, to which a sum of the first n terms of the considered progression unboundedly approximates at an unbounded increasing of number n.
		This is the infinitely decreasing geometric progression with the first term 3/10 and a common ratio q = 1/10.
	www.bymath.com /studyguide/alg/sec/alg29.html (373 words)

	"Golden" geometric progression
		On the one hand, the sequence (6) is "geometrical progression" because each term of (6) is equal previous one multiplied by constant for the given progression number of
		and such geometrical progression is called as the "golden" progression.
		In opinion of many researchers, the property (4), which is inherent only in the "golden" progression is the cause of widespread occurrence just of the "golden" equiangular spiral in the forms and structures of the alive nature.
	www.goldenmuseum.com /0205Progression_engl.html (347 words)

	Math Is Fun Forum / Algebra Formulas
		An Arithmetic Progression (AP) is a series in which the succesive terms have a common difference.
		The nth term of a Geometric Progression is given by
		A Harmonic Progression (HP) is is a series of terms where the reciprocals of the terms are in Arithmetic Progression (AP).
	www.mathsisfun.com /forum/viewtopic.php?pid=34876 (648 words)

	progressions and financial
		For conformity with the convention in the C language of computer programming, we take i to be in integer in the closed interval [0, n], where n is any given (fixed) non-negative integer.
		by Mathematical Induction, we have the arithmetic progression as the sequence
		It is the geometric series of the payments p -- for example, the repayment of a loan --, discounted by the interest-rate d = (r - 1):
	www.rism.com /Trig/progressions.htm (2189 words)

	[No title] (Site not responding. Last check: 2007-10-16)
		The number r is called the ratio of the progression, since it is the ratio (i.e., quotient) of a term to the preceding term.
		If the ratio r is negative, the terms of the geometric progression alternate in signs.
		In general, the geometric mean of n positive numbers is the nth root of their product.
	www.thiel.edu /mathproject/atps/chptr04/p022.htm (228 words)

	Geometric Progression
		Formula for the sum of the first n numbers of geometric progression
		Solution: Yes it is geometric progression with scale factor 2 and common ratio 2;
		Solution: there are two geometric progression the first one is with scale factor 1 and common ratio = 2
	www.math10.com /en/algebra/geometric-progression.html (244 words)

	Geometer's Angle no. 5 by Marcus the Marinite for the Nexus Network Journal vol.3 no.4 Autumn 2001 (Site not responding. Last check: 2007-10-16)
		However, if desired, the idea of the mean can be extended beyond its original sense of a particular type of middle place or term to comprise a progression for the purposes of enlarging or reducing elements in an orderly mathematical fashion, and especially for purposes of visual perspective, the diminution of forms in pictorial space.
		Applying a mean to determine a progression is quite simple in the case of the arithmetic and geometric means, but in the case of the harmonic mean, it is not nearly as straightforward.
		There may be philosophical questions regarding these physical qualities of music and harmony that the mathematics may suggest for the artist and the architect to explore in the manipulation and composition of forms in physical materials.
	www.nexusjournal.com /GA-v3n4.html (1190 words)

	MATHEMATICS DICTIONARY (Site not responding. Last check: 2007-10-16)
		The geometric average of nth positive numbers is the positive nth root of their product.
		The geometric average of two numbers is the middle term in a geometric progression of three terms including the two given numbers.
		The other terms of a geometric sequence of which the given numbers are the first and last terms; a single geometric mean between two positive numbers x and y is their geometric mean:
	lines-and-dots.org /g.html (328 words)

	Timepass: The Geometric Progression
		A geometric progression is a series of numbers, a(1), a(2), a(3), a(4)......
		For example, a geometric progression with the first term a(1) = 1 and common ratio 2 is:
		He was the one who realized the similarity between the geometric progression and this case.
	www.pha.jhu.edu /~sundar/tp/gp.html (703 words)

	461-3 Math Basics (Site not responding. Last check: 2007-10-16)
		A "progression" is a series of numbers created by some rule.
		Two common kinds of progressions are "arithmetic" and "geometric".
		In fact, the kind of curve created by a geometrical progression is called an "exponential curve".
	www.dxarts.washington.edu /dxarts/461-3/mathbasics (2044 words)

	Java: Arithmetic and Geometric Progression (Mathematics) - Development and miscellaneous! - by Dag Rune Sneeggen
		Here you have two classes, one for arithmetic and one for geometric progression.
		The second argument, d or k, is the difference in an arithmetic sequence and the common ratio in the geometric sequence.
		This little example happens to show why the mathematician who invented chess wanted his rice beans to double, as opposed to increase by two per square on the chess board!
	my.opera.com /duddev/blog/show.dml/295716 (269 words)

	Opinion - Geometric Progression
		This has further hindered progress in the quest for real-time analysis as more complex geometry naturally means more complex meshes.
		A model may contain geometric problems smaller than anything you can actually see; issues only arise when you try to do something with it.
		Geometric reasoning may well provide some of the answers.
	www.transcendata.com /pr20050320.htm (1934 words)

	Arithmetic progression - Wikipedia, the free encyclopedia
		In mathematics, an arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant.
		is an arithmetic progression with common difference 2.
		The sum of the components of an arithmetic progression is called an arithmetic series.
	en.wikipedia.org /wiki/Arithmetic_progression (471 words)

	geometric progression - HighBeam Encyclopedia (Site not responding. Last check: 2007-10-16)
		Find newspaper and magazine articles plus images and maps related to "geometric progression" at HighBeam.
		GEOMETRIC PROGRESSION ; The Portland painter's world of lines and shapes intersects with the Portland Museum of Art.
		Control Chart Tests Based on Geometric Moving Averages.
	www.encyclopedia.com /doc/1E1-x-geom-pro.html (149 words)

	Leon James 197x
		The 5 basic dialectic movements are indicated as the progression in five steps from levels I (white) to VI (fl).
		The first dialectic movement is represented by the progression from Stage 1 (white) to Stage 2 (yellow).
		For instance, the shape of a star is a configuration of 10 points connected continously on a plane surface.
	www.soc.hawaii.edu /leonj/499ss99/pederson/esnosys.html (560 words)

	A.P, G.P. Progressions - GMAT Math Sample Questions : 4GMAT - GMAT Practice Tests
		June 9, 2004: The sum of the fourth and twelfth term of an arithmetic progression is 20.
		What is the sum of the first 15 terms of the arithmetic progression?
		The Graduate Management Admission Council™ does not endorse, nor is it affiliated in any way with the owner or any content of this web site.
	questionbank.4gmat.com /mba_prep_sample_questions/ap_gp (193 words)

	randomendpoints \| geometric progression (Site not responding. Last check: 2007-10-16)
		The first number is the number you want the geometric progression to start with.
		The second number is the multiplier, the number you want each successive number to increment by.
		The third number is the number of integers you want in your progression.
	www.randomendpoints.com /c_code/gpsum.html (74 words)

	An AIDS Education Curriculum for ESL Students - Lesson 1 (Site not responding. Last check: 2007-10-16)
		One of the greatest deterrents to the practice of safer sex among teens and young adults is the mindset, "It can't happen to me." This lesson dramatizes the rapid geometric progression possible in the spread of HIV and helps students understand how exposure to possible infection or avoidance of infection is within their control.
		Students will become aware of the geometric patterns of infection in epidemics and see how rapidly HIV, as well as other sexually transmitted diseases (STDs), can be spread through unprotected intercourse.
		They will have the opportunity to imagine what it feels like to learn that they have been infected with an incurable, fatal disease, or to imagine what it feels like to learn that they have avoided infection by practicing safer sex.
	www.hostos.cuny.edu /homepages/lesnick/AIDS/page06.htm (1300 words)

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