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Topic: Plane (mathematics)

	Plane (mathematics) - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-05)
		In mathematics, a plane is a fundamental two-dimensional object.
		The topological plane, or its equivalent the open disc, is the basic topological neighbourhood used to construct surfaces (or 2-manifolds) classified in low-dimensional topology.
		The topological plane is the natural context for the branch of graph theory that deals with planar graphs, and results such as the four color theorem.
	en.wikipedia.org /wiki/Plane_(mathematics) (1083 words)

	Standards of Learning for Mathematics (Site not responding. Last check: 2007-11-05)
		Mathematics has its own language, and the acquisition of specialized vocabulary and language patterns is crucial to a student's understanding and appreciation of the subject.
		Mathematics Standards of Learning Geometry This course is designed for students who have successfully completed the standards for Algebra I. The course, among other things, includes the deductive axiomatic method of proof to justify theorems and to tell whether conclusions are valid.
		Mathematics Standards of Learning Advanced Placement Calculus This course is intended for students who have a thorough knowledge of analytic geometry and elementary functions in addition to college preparatory algebra, geometry, and trigonometry.
	www.pen.k12.va.us /go/Sols/math.html (14761 words)

	Plane - Wikipedia, the free encyclopedia
		Plane (mathematics), theoretical surface which has infinite width and length, zero thickness, and zero curvature
		Plane, Film (photography), the vertical or horizontal surface where film passes behind the lens.
		Plane (cosmology), a theoretical region beyond the known universe, or the region containing the universe itself
	en.wikipedia.org /wiki/Plane (218 words)

	AllRefer.com - plane (Mathematics) - Encyclopedia
		An example of a plane, or more exactly of a bounded portion of a plane, is the surface forming one face, or side, of a cube.
		A plane is determined, or defined, by any of the following: (1) three points not in a straight line; (2) a straight line and a point not on the line; (3) two intersecting lines; or (4) two parallel lines.
		For a given plane in space, a line can either lie outside and parallel to it, intersect the plane in a single point, or lie entirely in the plane; if more than one point of a straight line lies in the plane, then the entire line must lie in the plane.
	reference.allrefer.com /encyclopedia/P/plane.html (224 words)

	Mathematics and Art
		It also contains original mathematical results which again is very unusual in a book written in the style of a teaching text (although in the introduction Piero does say that he wrote the book at the request of his patron and friends and not as a school book).
		Leonardo distinguished two different types of perspective: artificial perspective which was the way that the painter projects onto a plane which itself may be seen foreshortened by an observer viewing at an angle; and natural perspective which reproduces faithfully the relative size of objects depending on their distance.
		The main theorem in Taylor's theory of linear perspective is that the projection of a straight line not parallel to the plane of the picture passes through its intersection and its vanishing point.
	www-groups.dcs.st-and.ac.uk /~history/HistTopics/Art.html (4272 words)

	Plane Patterns - 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.
		It is observed that 13 of the 17 plane patterns are represented at the Alhambra.
		There is a very useful chart on the seventeen plane patterns that clearly labels the locations of the centers of rotation (with labels that distinguish the 2, 3, 4, and 6-fold centers), the axes of reflection, and the axes of glide-reflection.
	math.truman.edu /~thammond/history/PlanePatterns.html (3146 words)

	On-line Mathematics Dictionary
		In particular, for a cone or pyramid, a frustum is determined by the plane of the base and a plane parallel to the base.
		The branch of mathematics that deals with the nature of space and the size, shape, and other properties of figures as well as the transformations that preserve these properties.
		A point of inflection of a plane curve is a point where the curve has a stationary tangent, at which the tangent is changing from rotating in one direction to rotating in the oppostie direction.
	www.mathpropress.com /glossary/glossary.html (4700 words)

	Colorful Mathematics: Part III (Site not responding. Last check: 2007-11-05)
		Furthermore, if a particular mathematical statement can be proven with a new technique, mathematicians are trained to try to look for new problems which might also be proven with this technique.
		A plane graph can be face-colored with exactly two colors if and only if the valence of all the vertices of the graph is even.
		Note that for plane graphs, the fact that bipartite graphs have only circuits of even length is reflected in the fact that each face of the graph has an even number of sides.
	www.ams.org /featurecolumn/archive/colour2.html (1074 words)

	Glossary - Content Standards (CA Dept of Education)
		Two shapes in the plane or in space are congruent if there is a rigid motion that identifies one with the other (see the definition of rigid motion).
		In geometry, a transformation D of the plane or space is a dilation at a point P if it takes P to itself, preserves angles, multiplies distances from P by a positive real number r, and takes every ray through P onto itself.
		The reflection through a line in the plane or a plane in space is the transformation that takes each point in the plane to its mirror image with respect to the line or its mirror image with respect to the plane in space.
	www.cde.ca.gov /be/st/ss/mthglossary.asp (1759 words)

	0300
		The course emphasizes manners in which mathematical models are constructed for physical problems and illustrates from many fields of endeavor, such as physical sciences, biology, and traffic dynamics.
		The course traces the development of mathematics and its applications from the Greek mathematicians through the modern age including the development of computer techniques in applied mathematics.
		Intensive study under the guidance of a member of the Computer and Mathematics faculty culminating in an individually researched and formally written report and oral presentation dealing with the applications of the mathematical sciences in the students area of specialization and related to one type of business or industry in the Houston area.
	cms.dt.uh.edu /CMSCourses/MathCourses.html (2424 words)

	Xah: Special Plane Curves: References (Site not responding. Last check: 2007-11-05)
		The course can serve either as the one undergraduate geometry course taken by mathematics majors in general or as a sequel to college geometry for prospective or current teachers of secondary school mathematics.
		Here's the description from the back cover: This is a genuine introduction to plane algebraic curves from a geometric viewpoint, designed as a first text for undergraduates in mathematics, or for postgraduate and research workers in the engineering and physical sciences.
		By adding points at infinity the affine plane is extended to the projective plane, yielding a natural setting for curves and providing a flood of illumination into the underlying geometry.
	www.xahlee.org /SpecialPlaneCurves_dir/Intro_dir/references.html (2840 words)

	Mathematics of Perspective Drawing
		Because light reflecting off the object travels in straight lines, the object point is seen on the drawing plane at the point where the line from the eyepoint to the object point intersects the drawing plane.
		This plane intersects the drawing plane in a line hence the image of a line in space is a line in the drawing.
		plane and on the circle plane is can't be on the circle, in fact it is farther from the center than any point of the circle, hence
	www.math.utah.edu /~treiberg/Perspect/Perspect.htm (5252 words)

	MATHEMATICS (Site not responding. Last check: 2007-11-05)
		Covers approximately the first half of MA 111, including analytic geometry in the plane, vectors in the plane, algebraic and transcendental functions, limits and continuity, and an introduction to differentiation.
		An introduction to techniques of mathematical modeling involved in the analysis of meaningful and practical problems arising in many disciplines including mathematical sciences, operations research, engineering, and the management and life sciences.
		A student must attend at least 10 mathematics seminars or colloquia and present one of the seminars, based on material mutually agreed upon by the instructor and the student.
	www.rose-hulman.edu /Catalog/ma_desc.htm (2459 words)

	FCIC: GED Information Bulletin
		Although 80% of the mathematics questions are multiple choice, 20% of the questions require you to construct your own answer.
		Both Parts I and II of the Mathematics Test have multiple-choice, standard grid, and coordinate plane grid questions.
		On the coordinate plane grid, make sure that you fill in only one circle to represent your answer.
	www.pueblo.gsa.gov /cic_text/education/ged/math.htm (1495 words)

	Body (Site not responding. Last check: 2007-11-05)
		This is the usual upper half plane model of the hyperbolic plane thought of as a map of the hyperbolic plane in the same way that we use planar maps of the spherical surface of the earth.
		Thus, we have established that the annular hyperbolic plane is the same as the usual upper half plane model of the hyperbolic plane.
		In the upper half plane model an ideal triangle is a triangle with all three vertices either on the x-axis or at infinity.
	www.math.cornell.edu /~dwh/papers/crochet/crochet.html (3801 words)

	Symmetry - Mathematics and the Liberal Arts
		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.
		It follows that mathematical chaos can be highly symmetric." He closes with a discussion of modern architecture, where he finds that symmetry concerns are important as well: "But the variety of historical reminiscences and asymmetrical elements in architecture does not mean a movement back to historicism or eclecticism.
		One minor comment is that a couple of times in the article she tells us that there is "no test or algorithm" that will answer a certain kind of question; it seems that she may actually mean only that there is no test or algorithm currently known.
	math.truman.edu /~thammond/history/Symmetry.html (6651 words)

	Illuminations: Covering the Plane with Rep-Tiles (Site not responding. Last check: 2007-11-05)
		Senechal (1990) notes that the study of tilings is important in mathematics education because the study of shape "draws on and contributes to not only mathematics but also the sciences and the arts." Some common uses of tilings include the covering of walls, floors, ceilings, streets, sidewalks, and patios.
		Consistent with Grunbaum and Shephard's (1987) definition, a tiling is a partitioning of the plane into regions, or tiles.
		The National Council of Teachers of Mathematics is a public voice of mathematics education, providing vision, leadership, and professional development to support teachers in ensuring mathematics learning of the highest quality for all students.
	illuminations.nctm.org /index_d.aspx?id=251 (1312 words)

	Mathematics Animated
		The horizontal line segment shown below the curve consists of copies of the segments that connect the foci with the moving point on the ellipse, showing that the sum of the two lengths is constant.
		Sometime around 1825, the Belgian geometers Adolphe Quetelet and Germinal Dandelin devised a simple and elegant construction showing that a plane that is parallel to a generator of the cone intersects that cone in a parabola.
		The Quetelet/Dandelin proof that a plane whose angle from the vertical is less than the vertex angle of a cone meets that cone in an ellipse.
	clem.mscd.edu /~talmanl/MathAnim.html (1785 words)

	Welcome to Math Central (Site not responding. Last check: 2007-11-05)
		Note: The definitions included here are those that are used in the Saskatchewan Education document "Mathematics 6-9: A Curriculum Guide for the Middle Level".
		These definitions are designed to be meaningful to middle level mathematics teachers.
		When graphed in the coordinate plane, it is the distance from the y-axis.
	mathcentral.uregina.ca /RR/glossary/middle (367 words)

	On False Convictions Concerning Geometric Transformations of the Plane In Mathematics Students’ Reasoning (Site not responding. Last check: 2007-11-05)
		I analysed these types of reasoning from the point of view of logic and mathematics in order to point out the essence of an error and its hypothetical sources.
		Assumptive foundations of mistaken reasoning existing in solutions of problems given by students I called false convictions which is analogous to observed by Bell (Bell, 1992) students’ false views.
		The example of observed students’ false conviction is distinguishing erroneous mental scheme referring to identifying the image of a line segment under a geometric transformation in the plane.
	www.icme-organisers.dk /tsg10/resumenes/Pawlik.html (345 words)

	Body (Site not responding. Last check: 2007-11-05)
		Now the circles are projected onto plane P as two curves emerging from the point S(x), the angle between these curves being equal to that between their tangent vectors.
		But the planes NKx and NLx intersect the plane Q parallel to the plane P, along the straight lines NK and NL, therefore the straight lines S(x)K´ and S(x)L´ are parallel, respectively to the lines NK and NL.
		Theorem 3: Every isometry of the plane is the composition of one, two or three reflections and is either the identity, a reflection, a rotation, a translation, or a glide reflection.
	www.math.cornell.edu /~dwh/papers/I-learn/I-learn.html (5280 words)

	Chapter 111. Subchapter B
		(1) Within a well-balanced mathematics curriculum, the primary focal points at Grade 6 are using ratios to describe proportional relationships involving number, geometry, measurement, and probability and adding and subtracting decimals and fractions.
		Throughout mathematics in Grades 6-8, students use these processes together with technology (at least four-function calculators for whole numbers, decimals, and fractions) and other mathematical tools such as manipulative materials to develop conceptual understanding and solve problems as they do mathematics.
		(1) Within a well-balanced mathematics curriculum, the primary focal points at Grade 7 are using proportional relationships in number, geometry, measurement, and probability; applying addition, subtraction, multiplication, and division of decimals, fractions, and integers; and using statistical measures to describe data.
	www.tea.state.tx.us /rules/tac/chapter111/ch111b.html (3144 words)

	Math Forum: Where's the Math? (Site not responding. Last check: 2007-11-05)
		California Math Show project, I have often been asked the question, "Where's the math?" As students explore mathematics through activities such as drawing tessellating patterns or forming tessellations with activity pattern blocks, it is important for teachers to emphasize mathematical ideas.
		One mathematical idea that can be emphasized through tessellations is symmetry.
		The Math Forum is a research and educational enterprise of the Drexel School of Education.
	mathforum.org /sum95/suzanne/wheremath.html (133 words)

	Mathematics (Site not responding. Last check: 2007-11-05)
		The Board of Education has taken an important step to raise the expectations for all students in Virginia's public schools by adopting new Standards of Learning in four core subject areas: mathematics, science, English, and history and social science.
		--------------------------------------------------------------------------- Mathematics Standards of Learning Kindergarten The kindergarten standards place emphasis on counting; combining, sorting, and comparing sets of objects; recognizing and describing simple patterns; and recognizing shapes and sizes of figures and objects.
		--------------------------------------------------------------------------- Mathematics Standards of Learning Grade Two The second-grade standards extend the study of number and spatial sense to include three-digit numbers and three-dimensional figures.
	pixel.cs.vt.edu /sol3.html (2490 words)

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