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Topic: Plane geometry

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	Euclidean geometry - Wikipedia, the free encyclopedia
		It is important to remember that, in the original and correct conception, geometry is, first of all, a physical science ("the noblest of the physical sciences"); that is, the logical definition of geometry (its fundamental assumptions or axioms) arises directly out of observation.
		In Hyperbolic geometry the sum of the three angles are always less than 180 and can approach zero.
		Tarski used his axioms to show Euclidean geometry is a complete decidable theory; that is, every proposition of Euclidean geometry can be shown to be either true or false.
	en.wikipedia.org /wiki/Plane_geometry (861 words)

	Euclidean geometry -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-06)
		Euclidean geometry in three dimensions is traditionally called (The geometry of 3-dimensional space) solid geometry.
		Plane geometry is the kind of (The pure mathematics of points and lines and curves and surfaces) geometry usually taught in (A public secondary school usually including grades 9 through 12) high school.
		Today, Euclidean geometry is usually constructed rather than ((logic) a proposition that is not susceptible of proof or disproof; its truth is assumed to be self-evident) axiomatized, by means of (The use of algebra to study geometric properties; operates on symbols defined in a coordinate system) analytic geometry.
	www.absoluteastronomy.com /encyclopedia/e/eu/euclidean_geometry.htm (954 words)

	Teaching Models: Grade 1
		The study of geometry focuses on space and the figures and shapes that are a part of space.
		Plane geometry concerns itself with the study of two-dimensional shapes, or figures that lie in a plane.
		A second goal of the study of geometry in the primary grades should be the gradual use of conventional terminology when students describe and discuss figures and shapes.
	www.eduplace.com /math/mw/models/overview/1_7_2.html (532 words)

	Wikipedia: Square
		In plane geometry, a square is a polygon with four equal sides and equal angles.
		In carpentry, a square is a guide for establishing right angles (ninety-degree angles), usually made of metal and in the shape of a right triangle.
		In the geometry narrative Flatland, A Square is the name of the main narrator of the story.
	www.factbook.org /wikipedia/en/s/sq/square.html (311 words)

	Nineteenth Century Geometry
		Today projective geometry does not play a big role in mathematics, but in the late nineteenth century it came to be synonymous with modern geometry.
		one may say that the truth of the geometry of Euclid is not incompatible with the truth of the geometry of Lobachevsky, for the existence of a group is not incompatible with that of another group.
		Geometry distinguishes itself from other natural sciences because it obtains only very few concepts and laws directly from experience, and aims at obtaining from them the laws of more complex phenomena by purely deductive means.
	plato.stanford.edu /entries/geometry-19th (4782 words)

	Plane Geometry Overview
		Plane Geometry is a proven package of related computer programs that assist the modeler in the preliminary design of model airplanes of all types including free flight, U-control, R/C power models and R/C sailplanes.
		Plane Geometry is a series of spreadsheets in the Microsoft Excel format.
		Plane Geometry is six separate spreadsheets and an instruction booklet.
	members.cox.net /evdesign/pages/plane_geometry.html (659 words)

	Building Blocks - Words - First Glance (Site not responding. Last check: 2007-11-06)
		Geometry is about the shape and size of things.
		These pictures show the four basic concepts on which the rest of geometry is built.
		A plane is a flat surface that extends endlessly in all directions.
	www.math.com /school/subject3/lessons/S3U1L1GL.html (128 words)

	Math 371 Geometry Notes on Line
		A lunar region in the plane is not convex.
		in the plane was used in the proof of the equidecomposable polygon theorem.
		The axioms for projective geometry in a plane uses two basic objects: points and lines, and a relation between those: a point is on a line, or a line passes through a point.
	www.humboldt.edu /~mef2/Courses/m371notes03.html (11762 words)

	Amazon.ca: Books: Schaum's Outline of Theory and Problems of Geometry: Includes Plane, Analytic, Transformational, and ... (Site not responding. Last check: 2007-11-06)
		Analytic geometry and transformational geometry has been added and the section on solid geometry shortened in line with the recent national curriculum changes.
		For plane geometry courses in high schools and colleges and for those who want independent self study.
		GEOMETRY contains 712 solved problems, with step-by-step solutions, concepts and proofs in plane geometry, trigonometry, and solid geometry, sample problems and help dealing with such complexities as trapezoids, regular polygons, methods of proof, and more.
	www.amazon.ca /exec/obidos/ASIN/0070522464 (586 words)

	51: Geometry
		Solid geometry is placed here (actually in 51M05) because it mirrors elementary plane geometry, but spherical geometry is primarily on the page for general convex geometry.
		Cabri-geometry is used for teaching secondary school geometry, but, equally important, is its use for university level instruction and as a tool by mathematicians in their research work.
		A useful collection of Geometry Formulas and Facts is taken from the CRC Standard Mathematical Tables and Formulas, and available at the The Geometry Center.
	www.math.niu.edu /~rusin/known-math/index/51-XX.html (828 words)

	Description of Focal Plane Geometry PIA Software Modules and Tools (Site not responding. Last check: 2007-11-06)
		The Focal Plane Geometry Map is analysed using modules which are integrated into the PIA software package as they comprise data analysis methods useful not only for the special application of focal plane geometry, but also for general astronomical data analysis.
		The main goal of the focal plane geometry map is to derive a corrected set of coordinates for the s/c pointing from a raster map of the PHT focal plane.
		The Focal Plane Geometry Cross Scans are supposed to confine the positional data for the PHT sub-instruments such that a final set of s/c offset parameters can be derived.
	isowww.estec.esa.nl /manuals/PHT/pia/um/fpg.html (2563 words)

	Plane (Site not responding. Last check: 2007-11-06)
		Reorients and positions the plane so that its intercepts with the x-, y-, and z-axes are the given values, respectively.
		If plane is parallel to a coordinate-axes plane, returns coordinate vectors (e.g., if parallel to x-y plane, returns unit vectors in x and y, respectively).
		Otherwise, returns one vector that follows the intersection of this plane and the x-y plane; the second vector is (uniquely) defined as perpendicular to both the normal and the first in-plane vector.
	www.ccr.buffalo.edu /etomica/doc/JavaDoc/etomica/math/geometry/Plane.html (926 words)

	R/C Soarer - Plane Geometry
		A great feature of Design is the ability to change, say, the yawing moment coefficient due to the vertical stabiliser, and see the vertical stab dimensions adjusted to suit on the 3-D plot.
		Plane Geometry has a 3-D Plot block facility which is available in both Measure and Design templates.
		A look at the summary in the Planes database shows that for similar configuration models, a value of around -.001 would be a better choice.
	www.rc-soar.com /hardsoft/planegeo.htm (1174 words)

	Plane Analytical Geometry :: Introduction (Site not responding. Last check: 2007-11-06)
		Analytic geometry, also called coordinate geometry and earlier referred to as Cartesian geometry, is the study of geometry using the principles of algebra.
		As taught in school books, analytic geometry can be explained more simply: it is concerned with defining geometrical shapes in a numerical way, and extracting numerical information from that representation.
		Rene Descartes introduced the foundation for the methods of analytic geometry in 1637 in the appendix titled GEOMETRY of the titled Discourse on the Method of Rightly Conducting the Reason in the Search for Truth in the Sciences, commonly referred to as Discourse on Method.
	analytical-geometry.net (290 words)

	The Geometry of the Sphere 1.
		It is easy to see that the circle of intersection will be largest when the plane passes through the center of the sphere, as it does in the figure to the left.
		In plane geometry the basic concepts are points and lines.
		Remember that a great circle is the intersection of the sphere with a plane that passes through the center of the sphere.
	math.rice.edu /~pcmi/sphere/sphere.html (667 words)

	Undefined: Points, Lines, and Planes
		The geometry of a saddle shaped surface is known as hyperbolic geometry (from the Greek to exceed).
		This geometry was popularized by Albert Einstein when he developed his theory of General Relativity with the notion that space is curved by the presence of mass.
		Given a plane in space, there exists at least one point in space that is not in the plane.
	www.andrews.edu /~calkins/math/webtexts/geom01.htm (2268 words)

	Plane Geometry (Site not responding. Last check: 2007-11-06)
		In approximately 300 B.C., Euclid (biography) laid the foundations for plane geometry in his book The Elements.
		Euclidean geometry is also known as flat geometry.
		century, alternate forms of geometry were developed, where lines are not straight.
	www.mathreference.com /geo,intro.html (189 words)

	Amazon.com: Books: Experiencing Geometry: On Plane and Sphere (Site not responding. Last check: 2007-11-06)
		In Experiencing Geometry on Plane and Sphere, Henderson invites readers to explore the basic ideas of geometry beyond the formulation of proofs.
		Key Benefit: In Experiencing Geometry on Plane and Sphere, Henderson invites readers to explore the basic ideas of geometry beyond the formulation of proofs.
		I used this book for a graduate level geometry class, and I found this book to be very enjoyable in terms of thinking that it requires and the way that the author presents the material.
	www.amazon.com /exec/obidos/tg/detail/-/0133737705?v=glance (502 words)

	Geometry: A Small Package for Mechanized (Plane) Geometry Manipulations Version 1.1 (ResearchIndex) (Site not responding. Last check: 2007-11-06)
		Abstract: Geometry is not only a part of mathematics with ancient roots but also a vivid area of modern research.
		Especially the field of geometry, called by some negligence "elementary", continues to attract the attention also of the great community of leisure mathematicians.
		This is probably due to the small set of prerequisites necessary to formulate the problems posed in this area and the erudition and non formal approaches ubiquitously needed to solve them.
	citeseer.ist.psu.edu /474637.html (325 words)

	History of Axioms (Site not responding. Last check: 2007-11-06)
		The axiom system we're using for Euclidean plane geometry is based on an axiom system introduced by George Birkhoff in the early 1920's.
		The difference between Birkhoff's axiom systems and earlier axiom systems for plane geometry is that his axioms use the real numbers and their properties.
		This is actually a very common viewpoint; for example, in modern geometry the concept of a "metric space" is fundamental.
	www.math.uga.edu /~clint/2004/5200/axioms/history.htm (600 words)

	Element classes and construction methods for the Geometry Applet
		In particular, [z] indicates z is an optional integer, and [plane A] indicates A is an optional plane.
		The optional data elements are only used in solid geometry; they should always be omitted in plane geometry.
		When an optional plane such as [plane A] is not specified, it is assumed to be the xy-plane.
	aleph0.clarku.edu /~djoyce/java/Geometry/tables.html (1189 words)

	Ethnomathematics Digital Library (EDL) (Site not responding. Last check: 2007-11-06)
		The objective of the research was “to know, understand and explain how a child in the early school years perceives its environment and explains it using concepts from geometry and isometry.” The section on Synthesis of the Teaching Material includes 6 activities with illustrations and diagrams.
		This study focuses on the plaited plane patterns that are evident in the twill-plaited baskets made by Tonga weavers in the coastal Inhambane province in southeast Mozambique.
		“In general, two plane patterns are considered instances of the same plane pattern if one can be transformed into the other by a (sequence of) rotation(s), translation(s), and/or reflection(s).” This report covers an interesting series of recently created plane patterns.
	www.ethnomath.org /search/browseResources.asp?type=subject&id=342 (1212 words)

	APPLICATIONS OF THE CLIFFORD-GRASSMANN ALGEBRA TO THE PLANE GEOMETRY (Site not responding. Last check: 2007-11-06)
		The applications of Clifford algebra to plane geometry are shown in two different but complementary cases: the Euclidean and pseudo-Euclidean planes.
		While the first expression reproduces and explains the standard use of the complex numbers in plane geometry, only the second one generalises to every dimension and to geometric elements of any order.
		Then we have got, combining the two plane geometric algebras, a unified account of both the circle and the hyperbola.
	www.terra.es /personal/rgonzal1/poster/poster.htm (1013 words)

	51M04: Elementary Euclidean geometry (2-dimensional)
		Ordinary plane geometry (such as is studied in US secondary schools) holds an irresistible appeal, although many results derive what appear to be unimaginative conclusions from tortured premises.
		Constructibility with compass and straightedge is dealt with elsewhere.
		Tilings and packings in the plane are part of Convex Geometry.
	www.math.niu.edu /~rusin/known-math/index/51M04.html (471 words)

	Geometry Requirements
		Present a high school transcript showing one year of geometry with a "C" average to the Math Assessment Coordinator.
		Present a college transcript showing the equivalent of MAT 053, Elementary Plane Geometry, with a grade of "pass" ("C" or better) to the Math Assessment Coordinator.
		Study geometry independently on-line1, on-line 2 and obtain approval to re-test from the Math Assessment Coordinator.
	www.oakton.edu /resource/iss/georeq.htm (185 words)

	Spherical Geometry
		Whereas basic plane geometry is concerned with points and lines and their interactions, most of the early geometry of the Babylonians, Arabs, and Greeks was spherical geometry--the study of the Earth, idealized as a sphere.
		A great circle ; on a sphere is the intersection of that sphere with a plane passing through the center of the sphere.
		The intersection of the plane determined by these points and the sphere is the great circle joining the two given points.
	www.math.uncc.edu /~droyster/math3181/notes/hyprgeom/node5.html (1398 words)

	The Geometry of the Sphere
		In plane geometry we study points, lines, triangles, polygons, etc. On the sphere we have points, but there are no straight lines --- at least not in the usual sense.
		However, straight lines in the plane are characterized by the fact that they are the shortest paths between points.
		We will study the incidence relations between great circles, the notion of angle on the sphere, and the areas of certain fundamental regions on the sphere, culminating with the area of spherical triangles.
	math.rice.edu /~pcmi/sphere (410 words)

	Plane Geometry and Other Affairs of the Heart, R. M. Berry
		Seven stories of Earth turned topsy-turvy, of Atlanta in flames, Florida under ice, of Adams, Eves, Pythagorean rock bands and Martin Heidegger's shortest speech, of rising into love, falling apart, of semihemidemiquavers, dodecahedrons, eigenvalues, quarks, of Milton's blindness, of sin's light, here in the Milky Way galaxy where whatever you fear might happen already has.
		During the great Pensacola blizzard a geometry teacher solaces his breaking heart building trapezoids from the floorboards of his snow-filled home; on his thirteenth birthday, Harry Sneltzer wakes to discover that he's been metamorphosed into his own dad.
		All these affairs take shape just above the dark plane of seem and be, in the heart's interstice, within a geometry book as convoluted as desire, where each constellation becomes another, where ends are all beginnings, where everything is up in the air.
	nupress.northwestern.edu /title.cfm?ISBN=0-914590-88-X (213 words)

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