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	Similarity (mathematics) - Wikipedia, the free encyclopedia
		A similarity is a composition of a homothety and an isometry.
		Suppose that triangle ABC is similar to triangle DEF in such a way that the angle at vertex A is congruent with the angle at vertex D, the angle at B is congruent with the angle at E, and the angle at C is congruent with the angle at F.
		Similarity of matrices does not depend on the base field: if L is a field containing K as a subfield, and A and B are two matrices over K, then A and B are similar as matrices over K if and only if they are similar as matrices over L.
	en.wikipedia.org /wiki/Similarity_(mathematics) (1162 words)

	Similarity (mathematics): Definition and Links by Encyclopedian.com - All about Similarity (mathematics) (Site not responding. Last check: 2007-11-06)
		For example, all circles are similar, as are all squares.
		Similar matrices share many properties: they have the same determinant, the same trace, the same eigenvalues (but not necessarily the same eigenvectors), the same characteristic polynomial and the same minimal polynomial.
		If in the definition of similarity, the matrix P can be choses to be a permutation matrix then A and B are permutation-similar; if P can be chosen to be a unitary matrix then A and B are unitarily equivalent.
	www.encyclopedian.com /si/Similar.html (392 words)

	Similarity (mathematics) -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-06)
		On the other hand, (A closed plane curve resulting from the intersection of a circular cone and a plane cutting completely through it) ellipses are not all similar to each other, nor are (An open curve formed by a plane that cuts the base of a right circular cone) hyperbolas all similar to each other.
		Two (A three-sided polygon) triangles are similar if and only if they have the same three (The space between two lines or planes that intersect; the inclination of one line to another; measured in degrees or radians) angles, the so-called "AAA" condition.
		The similarity is a function such as its value is greater when two points are closer (contrarly to the distance, which is a measure of disimilarity: the closer the points, the lesser the distance).
	www.absoluteastronomy.com /encyclopedia/S/Si/Similarity_(mathematics).htm (837 words)

	Interactive Mathematics Dictionary - Similarity Definitions
		According to the AA similarity property, to show two triangles are similar, it is sufficient to verify that two angles of one triangle are congruent to the corresponding angles of another triangle.
		According to the SAS similarity property, to show two triangles are similar, it is sufficient to verify that the measures of two sides of a triangle are proportional to the measures of two corresponding sides of another triangle, and the included angles are congruent.
		According to the SSS similarity property, to show two triangles are similar, it is sufficient to verify that the measures of the three sides of one triangle are proprotional to the corresponding measures of the sides of another triangle.
	www.intermath-uga.gatech.edu /tweb/gwin1-01/apley/Dictionary/Similarity/similarity.html (693 words)

	Homothetic transformation - Wikipedia, the free encyclopedia
		In mathematics, a homothety (or homothecy) is a transformation of space which dilates distances with respect to a fixed point A called the origin.
		The number c by which distances are multiplied is called the dilation factor or similitude ratio.
		A homothety is an affine transformation (if the fixed point is the origin: a linear transformation) and also a similarity transformation.
	en.wikipedia.org /wiki/Homothety (156 words)

	Overview of Mathematics (Site not responding. Last check: 2007-11-06)
		Mathematics (from Greek mathema: science, knowledge, learning; mathematikos: fond of learning) is the study of patterns of quantity, structure, change and space.
		Calculus is concerned with concepts such as the rate of change of one variable quantity with respect to another, the slope of a curve at a prescribed point, the computation of the maximum and minimum values of functions, and the calculation of the area bounded by curves.
		Logic is regarded as a branch both of philosophy and of mathematics.
	kosmoi.com /Science/Mathematics (917 words)

	Similarity (mathematics)
		Two geometrical objects are called similar if both have the same shape.
		For example, all circles are similar to each other, all squaress are similar to each other, and all parabolas are similar to each other.
		In order for two triangles to be similar, it is sufficient for then to have at least two angles that match.
	pedia.newsfilter.co.uk /wikipedia/s/si/similarity__mathematics_.html (701 words)

	Project MATHEMATICS!
		produces videotape-and-workbook modules that explore basic topics in high school mathematics in ways that cannot be done at the chalkboard or in a textbook.
		Similarity Scaling multiplies lengths by the same factor and produces a similar figure.
		Early History of Mathematics This 30-minute videotape traces some of the landmarks in the early history of mathematics--from Babylonian clay tablets produced some 5000 years ago, when calendar makers calculated the onset of the seasons--to the development of calculus in the seventeenth century.
	www.projectmathematics.com (799 words)

	EPAA Vol. 9 No. 33 Zabulionis: Mathematics and Science Achievement of Various Nations
		Among all 41 countries having taken the TIMSS mathematics test for the upper grade, the highest similarity of the mathematics achievement profiles was found for England and Scotland.
		It was not unexpected that France in mathematics was most similar to the French part of Belgium (Belgium took the part in TIMSS education with two subsystems – Flemish and French, according to the prevalent language used in education in the country).
		Switzerland was similar to Germany in science (0.54), together with France (0.50), Norway (0.49) in Chemistry and to the Netherlands in Physics (0.42).
	epaa.asu.edu /epaa/v9n33 (4717 words)

	Mathematics - Geometry (Site not responding. Last check: 2007-11-06)
		Likewise, mathematics assessment must address the understanding of all students (as assessed with accommodations which match instructional methodologies) so that mathematics instruction can be evaluated and improved for all students.
		Mathematics should be viewed as a unified whole made up of connected, big ideas rather than as a disjointed collection of meaningless, abstract ideas and skills.
		Mathematics is important because its concepts and procedures can be applied to the solution of problems of varying kinds and complexity.
	www.indps.k12.wi.us /DISTRICT/GL16485.HTM (1812 words)

	Project MATHEMATICS!--Similarity (Site not responding. Last check: 2007-11-06)
		Another application of similarity explains why the sum of the angles in any triangle is a straight angle.
		Similarity is discussed for more general polygons and for three-dimensional objects.
		Similarity helps explain why a hummingbird's heart beats so much faster than a human heart, and why it is impossible for a small creature such as a praying mantis to become as large as a horse.
	www.projectmathematics.com /similar.htm (224 words)

	Self Similarity In Mathematics and Nature
		Even if the students have heard of (the mathematical sense of) similarity before, they are likely not to remember it too well.
		In any event, it is important that they understand what we mean by similarity in order for self similarity to have meaning, but it is also important not to get bogged down in defining similiarity precisely at this point.
		Tell the students that the concept of self similarity and self simillar objects have recently caught the attention of biologists, chemists, meteorologists, artists, musicians, and t-shirt manufacturers.
	storm.shodor.org /snowflake/help_docs/self_sim_lesson.html (799 words)

	International Conference on "The Unity of Mathematics" : Israel Gelfand's Talk at Royal East (Site not responding. Last check: 2007-11-06)
		There is also another side of the similarity between mathematics and classical music, poetry, and so on.
		An important side of mathematics is that it is an adequate language for different areas: physics, engineering, biology.
		For example, to use quantum mechanics in biology is not an adequate language, but to use mathematics in studying gene sequences is an adequate language.
	www-math.mit.edu /conferences/unityofmathematics/talks/gelfand-royal-talk.html (724 words)

	Similarity - Mathematics and the Liberal Arts
		The Mathematics and the Liberal Arts pages are intended to be a resource for student research projects and for teachers interested in using the history of mathematics in their courses.
		Although this brief excerpt does not mention it, it is not uncommon for the construction to be repeated in the same tracery in a different scale---a kind of reaching to infinity that is reminiscent of fractals.
		The author touches on (to give a few examples) interlace patterns (often considered to be connected with weaving), similarity symmetry, symmetries in higher dimensional spaces, and on some of the ideas of the theory of tilings, including Penrose tilings and hyperbolic tilings.
	math.truman.edu /~thammond/history/Similarity.html (612 words)

	FIELD THEORIES: PHYSICAL FIELDS
		This type of field theory is similar to my description of perception, where each percept is a point in psychological space that is a function of the components (which are, in effect, space-time axes) of that space.
		Note the close conceptual similarity (the mathematics would be different) to my description in Chapter 18 of the dependence of a person's behavior toward another on distances between them in the psychological field.
		I stress "conceptual" because the mathematical functions connecting dynamic events in the intentional field differ from those in the fields of nature, although the conceptual essenses of the fields are similar.
	www.hawaii.edu /powerkills/DPF.CHAP2.HTM (3728 words)

	Aristotle -- General Introduction [Internet Encyclopedia of Philosophy]
		The soul manifests its activity in certain "faculties" or "parts" which correspond with the stages of biological development, and are the faculties of nutrition (peculiar to plants), that of movement (peculiar to animals), and that of reason (peculiar to humans).
		These faculties resemble mathematical figures in which the higher includes the lower, and must be understood not as like actual physical parts, but like such aspects as convex and concave which we distinguish in the same line.
		This is similar to Aristotle's explanation of the use of orgiastic music in the worship of Bacchas and other deities: it affords an outlet for religious fervor and thus steadies one's religious sentiments.
	www.utm.edu /research/iep/a/aristotl.htm (7053 words)

	Amazon.ca: Books: Gnomon: From Pharaohs to Fractals (Site not responding. Last check: 2007-11-06)
		Among the most pleasing results of this chapter is his demonstration of the mirrored similarity in the appearance of numbers as they are represented by continued fractions, and as they are represented by our traditional positional number system.
		This is followed by explicit formulae for the terms of the sequence and even a demonstration of how some of these equations, in the limit, model the behavior of wave propagation in an electronic transducer ladder, and the movement of a ganged series of pulleys.
		While Gazale does not dive in with the sort of mathematical rigor to which a pure mathematician would aspire, he claims to have written an unusual chapter on the subject, derived directly from number-theoretic considerations.
	www.amazon.ca /exec/obidos/ASIN/0691005141 (1846 words)

	The Fractal Microscope (Site not responding. Last check: 2007-11-06)
		Extending beyond the typical perception of mathematics as a body of sterile formulas, fractal geometry mixes art with mathematics to demonstrate that equations are more than just a collection of numbers.
		But beyond potential applications for describing complex natural patterns, with their visual beauty fractals can help alter students' beliefs that mathematics is dry and inaccessible and may help to motivate mathematical discovery in the classroom.
		There are definitely uses for fractals within the classroom, such as introducing similarity (although the Mandelbrot set is only quasi self-similar), density, infinity, vector addition, division and reduction of fractions, scale and magnification, and pattern discovery.
	archive.ncsa.uiuc.edu /Edu/Fractal/Fractal_Home.html (645 words)

	The Math Forum - Math Library - History/Biography (Site not responding. Last check: 2007-11-06)
		A videotape-and-workbook module that explores a basic topic in high school mathematics in ways that cannot be done at the chalkboard or in a textbook.
		An exhibit on mathematics teaching devices from the Smithsonian's National Museum of American History, focusing on innovations in mathematics teaching from the flboard to graphing calculators and computer software.
		He had published no mathematical or astronomical works during his lifetime, but he left his papers in reasonably good order and set out his wishes in his will that they should be properly edited and published.
	mathforum.org /library/topics/history?...&start_at=551&num_to_see=50 (2132 words)

	mathematics similarity and trigonometry (Site not responding. Last check: 2007-11-06)
		The learner will be able to apply the concepts and properties of congruence and similarity.
		This is the first course in the Practical Mathematics Series 12061220613206.
		This course includes the topics which are similar to those of Mathematics 1204.
	learning-gd.com /articles/321/mathematics-similarity-and-trigonometry.html (149 words)

	Mad Papers, Term papers, Vol.49, Pg.5, 051020
		Game theory is described here as a mathematical formula that asseses outcomes of situations based on people's choices and the author of this paper sees Kubrick's film as an example of how outcomes are effected by particular choices.
		Procedural knowledge-or more appropriately skills-refers to the ability to physically solve a problem through the manipulation of mathematical skills: with pencil and paper, calculator, computer, etc. There is thus, in a theoretical sense, a difference between conceptual and procedural knowledge in mathematics.
		Thus, Both mathematics and language are governed by particular rules that are syntactically or structurally similar.
	www.madpapers.snrinfo.net /lib/essay/49_5.html (1326 words)

	Self-similarity (Site not responding. Last check: 2007-11-06)
		Self-similarity is, in my view, one of the most powerful analytical tools to come along in a lone time.
		As we upgrade our mathematical metaphors with the previous covered aspects of complexity theory, we can tuck self-similarity into our bag of tricks.
		Moving from mathematics to sociology and theology, we retain the factor that within a system we may find small and large versions of the same thing.
	www.intelligentchristian.org /Self-similarity.htm (461 words)

	IAM Faculty by Name
		Mathematical biology; dynamics of actin filaments in the cytoskeleton; swarming behaviour; type 1 diabetes
		Observational studies and mathematical modelling of micro- and mesoscale flow and turbulence phenomena in the atmospheric boundary layer; atmospheric pollution
		Scattering theory; mathematical and computer simulation of gas phase molecular reaction dynamics, and molecules in intense laser fields [selected publications]
	www.iam.ubc.ca /people/faculty/faculty.html (1044 words)

	NTTI Lesson: DEFEATING "MANHOLE MONSTERS" BY SIMILARITY
		PAUSE the video after the narrator says, "If the scaling factor is s then the perimeter of the triangle will be..." Have students finish the sentence.
		The end product will not be known to the students until they have each contributed their enlarged pieces of the puzzle.
		The students should have prior knowledge of similar figures having the same shape, scaling factors, area, perimeter, volume, the distributive law, and simple powers.
	www.thirteen.org /edonline/nttidb/lessons/13/dfeat13.html (1167 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		] A warp knitting machine that is similar to a tricot machine, but employs two sets of needles and knits a double fabric.
		A method of approximating a definite integral over an interval which is equivalent to dividing the interval into equal subintervals and applying the formula in the first definition to each subinterval.
		] A mathematical relationship for calculating the oil- or gas-bearing net-pay volume of a reservoir; uses the contour lines from a subsurface geological map of the reservoir, including gas-oil and gas-water contacts.
	www.accessscience.com /Dictionary/S/S27/DictS27.html (2717 words)

	ACCLAIM RI \| Library \| NECS List (Site not responding. Last check: 2007-11-06)
		Title: Mathematics proficiency of 12th-grade students, by selected student and school characteristics: 1996 and 2000 (table format)
		Size: 90.8 KB Title: Mathematics proficiency of 8th-grade students in public schools, by selected characteristics and state: 1992 and 1996 (graph)
		Title: Mathematics proficiency of 4th-grade students, by selected student and school characteristics: 1996 and 2000 (table format)
	acclaim.coe.ohiou.edu /rc/rc_sub/vlibrary/6_nces/list.asp (221 words)

	The Show-Me Standards (Site not responding. Last check: 2007-11-06)
		In Mathematics, students in Missouri public schools will acquire a solid foundation which includes knowledge of
		geometric and spatial sense involving measurement (including length, area, volume), trigonometry, and similarity and transformations of shapes
		mathematical systems (including real numbers, whole numbers, integers, fractions), geometry, and number theory (including primes, factors, multiples)
	www.dese.state.mo.us /standards/math.html (113 words)

	Glencoe Mathematics - Online Study Tools
		Of the movies Sally went to last year, 10 were comedies and 2 were dramas.
		Find the value of x in the pair of similar polygons.
		Which one of the triangles shown is not similar to the others?
	www.glencoe.com /sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-02-825275-6&chapter=7 (106 words)

	Amazon.com: Books: Scaling, Self-similarity, and Intermediate Asymptotics : Dimensional Analysis and Intermediate ... (Site not responding. Last check: 2007-11-06)
		It is demonstrated that scaling comes on a stage when the influence of fine details of initial and/or boundary conditions disappeared but the system is still far from ultimate equilibrium state (intermediate asymptotics).
		We say without thinking that the mass of water in a glass is 200 grams, the length of a ruler is 0.25 metres, the half-life of radium is 1 600 years, the speed of a car is 60 miles per hour.
		Barenblatt's book, Scaling, self similarity and intermediate asymptotics, addresses the understanding of physical processes and the interpretation of calculations revealing these processes, two mental problems intertwined closely with the deeper more general issues raised by the recognition of patterns.
	www.amazon.com /exec/obidos/tg/detail/-/0521435226?v=glance (1424 words)

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