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Topic: Geometry


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  Euclid's Elements, Introduction
The text of all 13 Books is complete, and all of the figures are illustrated using the Geometry Applet, even those in the last three books on solid geometry that are three-dimensional.
I often hear that geometry is no longer taught well here in the United States high schools.
One contributing factor, perhaps the major contributing factor, to the downfall of geometry education in the United States is the way it is presented in text books.
aleph0.clarku.edu /~djoyce/java/elements/elements.html   (416 words)

  
  PlanetMath: geometry
Geometry, or literally, the measurement of land, is among the oldest and largest areas of mathematics.
Gauss' theorem that the intrinsic geometry of the sphere could not possibly be the same as that of the plane and cylinder.
The discovery of intrinsic geometry led thoughtful geometers such as Riemann (who was a student of Gauss), Clifford, and Mach to the conclusion that a “right and natural” approach to geometry should regard surfaces as geometrical spaces in their own right on a par with Euclidean and projective space.
planetmath.org /encyclopedia/EuclideanGeometry.html   (4302 words)

  
  Geometry - Wikipedia, the free encyclopedia
Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers.
Early geometry was a collection of empirically discovered principles concerning lengths, angles, areas, and volumes, which were developed to meet some practical need in surveying, construction, astronomy, and various crafts.
The successors of Muḥammad ibn Mūsā al-Ḵwārizmī (born 780) undertook a systematic application of arithmetic to algebra, algebra to arithmetic, both to trigonometry, algebra to the Euclidean theory of numbers, algebra to geometry, and geometry to algebra.
en.wikipedia.org /wiki/Geometry   (4343 words)

  
 Geometry
The phrase "discrete geometry," which at one time stood mainly for the areas of packing, covering, and tiling, has gradually grown to include in addition such areas as combinatorial geometry, convex polytopes, and arrangements of points, lines, planes, circles, and other geometric objects in the plane and in higher dimen­sions.
Similarly, "computational geometry," which referred not long ago to simply the design and analysis of geometric algorithms, has in recent years broadened its scope, and now means the study of geometric problems from a computational point of view, including also computational convexity, computational topology, and ques­tions involving the combinatorial complexity of arrangements and polyhedra.
A difficulty usually found at the beginning of courses that build a geometry upon a set of postulates is to have the students understand that results derived from these postulates hold in some of the non‑Euclidean geometries as well, and therefore their proofs cannot rely on facts obtained from their drawings.
www.wordtrade.com /science/mathematics/geometry.htm   (6586 words)

  
 GEOMETRY - LoveToKnow Article on GEOMETRY
Pythagoras (q.v.), seeking the key of the universe in arithmetic and geometry, investigated logically the principles underlying the, known propositions; and this resulted in the formulation of definitions, axioms and postulates which, in addition to founding a science of geometry, permitted a crystallization, fractional, it is true, of the amorphous collection of material at hand.
Pythagorean geometry was essentially a geometry of areas and solids; its goal was the regular solids the tetrahedron, cube, octahedron, dodecahedron and icosahedronwhich symbolized the five elements of Greek cosmology.
The geometry of the circle,, previously studied in Egypt and much more seriously by Tbales, was somewhat neglected, although this curve was regarded as the most perfect of all plane figures and the sphere the most perfect of all solids.
www.1911encyclopedia.org /G/GE/GEOMETRY.htm   (21277 words)

  
 Geometry - MSN Encarta
Geometry may be thought of as the science of space.
Basic geometry allows us to determine properties such as the areas and perimeters of two-dimensional shapes and the surface areas and volumes of three-dimensional shapes.
People use formulas derived from geometry in everyday life for tasks such as figuring how much paint they will need to cover the walls of a house or calculating the amount of water a fish tank holds.
encarta.msn.com /encyclopedia_761569706/Geometry.html   (518 words)

  
 Functional group geometry
Molecular geometry is associated with the specific orientation of bonding atoms.
As in the water molecule there are two lone pairs of electrons on the oxygen in addition to the single bonds (invisible in the graphic), which give an electron pair geometry of tetrahedral.
As in the ammonia molecule there is one lone pair of electrons on the nitrogen in addition to the single bonds (invisible in the graphic), which give an electron pair geometry of tetrahedral.
www.elmhurst.edu /~chm/vchembook/522funcgpC.html   (749 words)

  
 Science> Mathematics> Geometry [encyclopedia]   (Site not responding. Last check: )
Geometry is concerned with the properties of space and of objects in space, e.g.
In its most elementary form geometry is concerned with such metrical problems as determining the areas and diameters of two-dimensional figures and the surface areas and volumes of solids.
The discovery of non-Euclidean geometries inspired a new approach to the subject by presenting theorems in terms of axioms applied to properties assigned to undefined elements called points and lines, not necessarily limited to the classical study of flat surfaces (plane geometry) and rigid three-dimensional objects (solid geometry).
www.kosmoi.com /Science/Mathematics/Geometry   (903 words)

  
 Non-Euclidean geometry
Lambert noticed that, in this new geometry, the angle sum of a triangle increased as the area of the triangle decreased.
Elementary geometry was by this time engulfed in the problems of the parallel postulate.
It is important to realise that neither Bolyai's nor Lobachevsky's description of their new geometry had been proved to be consistent.
www-groups.dcs.st-and.ac.uk /~history/HistTopics/Non-Euclidean_geometry.html   (1843 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)

  
 Amazon.com: Geometry: Books: David A. Brannan,Matthew F. Esplen,Jeremy J. Gray   (Site not responding. Last check: )
During the last third of the book (the chapters on hyperbolic and spherical geometry), some basic familiarity with trigonometric functions and hyperbolic functions is assumed (cosh, sinh, tanh, and their inverses).
In the eighth chapter all of these geometries are demonstrated to be special cases of the Kleinian vieuw of geometry: that is, every geometry can be seen as consisting of the invariants of a specific group of transformations of the 2 dimensional plane into itself.
And, by passing to the more abstract Projective geometry, you can express the abstract idea of 'conic' by giving just one quadratic curve, be it a parabola, ellipse or hyperbola, by the pair (Qu, P), whereby P is the group of all projective transformations.
www.amazon.com /Geometry-David-Brannan/dp/0521597870   (2970 words)

  
 Geometry Calculators
Plots & Geometry -- The equation of a line, plotting conic sections, graphing and plotting, and geometrical objects.
Java Gallery of Interactive Geometry -- A number of geometry Java applets -- hyperbolic triangles, simulation of the Lorenz equations, interation of a quadratic map, a version of the Tetris game, Leap fractal chaos game, creating and animating fractals, generate wallpaper patterns.
Geometry -- A geometry text covering points, lines, planes, angles, postulates and theorems, unions and intersections, formulas, constructions, etc. Contains sample problems and a comprehensive glossary.
www.ifigure.com /math/geometry/geometry.htm   (358 words)

  
 Geometry Solution
Geometry Solutions is a sophisticated calculator that calculates the perimeter, lateral and surface areas, and volume of plane and solid geometric figures.
For example, when you type in the angle, side, or the hypotenuse of a right angle, Geometry Solutions will calculate the perimeter and area based on the information you entered.
Geometry Solutions and geometric formulas when used together will strengthen your knowledge and abilities in geometry.
www.gomath.com /geometrycal.html   (159 words)

  
 The Geometry Applet
This geometry applet is being used to illustrate
Another example using this Geometry Applet illustrates the Euler line of a triangle.
The Geometry Applet uses a Slate Canvas put all the Elements on.
aleph0.clarku.edu /~djoyce/java/Geometry/Geometry.html   (899 words)

  
 Mathematics Archives - Topics in Mathematics - Geometry
Geometry Building Blocks, Geometry words, Coordinate geometry, Pairs of lines, Classifying angles, Angles and intersecting lines, Circles, Polygons, Triangles, Quadrilaterals, Area of polygons and circles, Congruent figures, Similar figures, Squares and square roots, The Pythagorean Theorem and right triangle facts, Three-dimensional Figures, Prisms, Pyramids, Cylinders, cones, and spheres
Spherical Geometry, Logic and the Axiomatic Method Incidence Geometry, Betweenness Axioms, Congruence Theorems, Axioms of Continuity, Neutral Geometry, Hyperbolic Geometry, Classification of Parallels, Inversion in Euclidean Circles, Models of Hyperbolic Geometry, Hypercycles and Horocycles, The Pseudosphere, Hyperbolic Trigonometry, Hyperbolic Analytic Geometry
Geometry, spatial-visualization skills, congruency, similarity, symmetry, area of polygons
archives.math.utk.edu /topics/geometry.html   (1366 words)

  
 Geometry Step by Step from the Land of the Incas, Intro, Cuzco, Machu Picchu
Geometry Step by Step from the Land of the Incas, Intro, Cuzco, Machu Picchu
Activate Flash plugin or Javascript and reload to view the Intro of Geometry from the Land of the Incas.
The Incas built a notable civilization in western South America in the fifteenth and sixteenth centuries.
agutie.homestead.com   (141 words)

  
 Cynthia Lanius' Lessons: Geometry Online
Thanks to PBS for permission to use the Pyramid photo.
Students will find line segments that they can and cannot draw of various irrational lengths, and then find the rule that allows them to draw or not draw.
The Texas Essential Skills and Knowledge - What the Texas Education Agency specifies students should know and be able to do from this course.
math.rice.edu /~lanius/Geom   (251 words)

  
 Mathematics Archives - Topics in Mathematics - Differential Geometry
Differential Geometry and Quantum Physics, SFB 288, TU Berlin
GRTensor II Calculation of tensor components on curved spacetimes specified in terms of a metric or set of basis vectors.
Lecture notes for the course in Differential Geometry
archives.math.utk.edu /topics/differentialGeom.html   (318 words)

  
 The Geometry Center Welcome Page
Users can rotate, scale, and translate the objects interactively with the mouse.
What Was New at the Geometry Center(as of 26 March 1998)
The University of Minnesota is an equal opportunity educator and employer.
www.geom.uiuc.edu   (115 words)

  
 Geometry
This is where you'll find almost everything you'll ever need to know about Geometry.
We have a special page on constructions and plenty of sample problems to help you understand the concepts.
Greek Prefixes for polygons/polyhedra (from Virtual Polyhedra, a GREAT geometry site)
library.thinkquest.org /2647/geometry/geometry.htm   (67 words)

  
 Computational Geometry Pages
Welcome to the Computational Geometry Pages, a (hopefully) comprehensive directory of computational geometry resources both on and off the Internet.
If there is something you'd like to see here, please send me email.
(a newsletter with events and announcements), David Eppstein's Geometry in Action (describing applications of computational geometry in the Real World), and the Los Alamos e­print archive's collection of computational geometry papers
compgeom.cs.uiuc.edu /~jeffe/compgeom   (224 words)

  
 Interactive Mathematics Miscellany and Puzzles, Geometry
Experimentation with Dynamic Geometry Software: An Example [Java]
The Chaos Game: Address Space vs IFS [Java]
Triangles, Squares and Areas from Temple Geometry [Java]
www.cut-the-knot.org /geometry.shtml   (844 words)

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