61. ThinkQuest : Library : Math For Morons Like Us lived way back in the 6th century BC (back when Bob Dole was learning geometry), came up with one of the most famous theorems ever, the Pythagorean theorem. http://library.thinkquest.org/20991/geo/stri.html

Index Math Math for Morons like Us Have you ever been stuck on math? If it was a question on algebra, geometry, or calculus, you might want to check out this site. It's all here from pre-algebra to calculus. You'll find tutorials, sample problems, and quizzes. There's even a question submittal section, if you're still stuck. A formula database gives quick access and explanations to all those tricky formulas. Languages: English. Visit Site 1998 ThinkQuest Internet Challenge Languages English Students J. Robert Davis High School Library, Kaysville, UT, United States John Davis High School Library, Kaysville, UT, United States Garrett Davis High School Library, Kaysville, UT, United States Coaches Jeff Davis High School Library, Kaysville, UT, United States Want to build a ThinkQuest site? The ThinkQuest site above is one of thousands of educational web sites built by students from around the world. Click here to learn how you can build a ThinkQuest site. Privacy Policy

62. Pythagorean Theorem -- From MathWorld Curious and Interesting geometry. London Penguin, pp. 202207, 1991. Yancey, B. F. and Calderhead, J. A. New and Old Proofs of the Pythagorean theorem. Amer http://mathworld.wolfram.com/PythagoreanTheorem.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index ABOUT THIS SITE About MathWorld About the Author DESTINATIONS What's New MathWorld Headline News Random Entry ... Live 3D Graphics CONTACT Email Comments Contribute! Sign the Guestbook MATHWORLD - IN PRINT Order book from Amazon Geometry Plane Geometry Triangles ... Triangle Properties Pythagorean Theorem For a right triangle with legs a and b and hypotenuse c Many different proofs exist for this most fundamental of all geometric theorems. The theorem can also be generalized from a plane triangle to a trirectangular tetrahedron , in which case it is known as de Gua's theorem . The various proofs of the Pythagorean theorem all seem to require application of some version or consequence of the parallel postulate : proofs by dissection rely on the complementarity of the acute angles of the right triangle, proofs by shearing rely on explicit constructions of parallelograms, proofs by similarity require the existence of non-congruent similar triangles, and so on (S. Brodie). Based on this observation, S. Brodie has shown that the parallel postulate is equivalent to the Pythagorean theorem.

63. Pascal's Theorem -- From MathWorld Coxeter, H. S. M. and Greitzer, S. L. Pascal s theorem. §3.8 in geometry Revisited. Washington, DC Math. Assoc. Amer., pp. 7476, 1967. http://mathworld.wolfram.com/PascalsTheorem.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index ABOUT THIS SITE About MathWorld About the Author DESTINATIONS What's New MathWorld Headline News Random Entry ... Live 3D Graphics CONTACT Email Comments Contribute! Sign the Guestbook MATHWORLD - IN PRINT Order book from Amazon Geometry Line Geometry Incidence ... Barile Pascal's Theorem The dual of Brianchon's theorem (Casey 1888, p. 146), discovered by B. Pascal in 1640 when he was just 16 years old (Leibniz 1640; Wells 1986, p. 69). It states that, given a (not necessarily regular , or even convex hexagon inscribed in a conic section , the three pairs of the continuations of opposite sides meet on a straight line , called the Pascal line -gon inscribed in a conic section are collinear, then the same is true for the remaining point. Braikenridge-Maclaurin Construction Brianchon's Theorem Cayley-Bacharach Theorem Conic Section ... search Casey, J. A Sequel to the First Six Books of the Elements of Euclid, Containing an Easy Introduction to Modern Geometry with Numerous Examples, 5th ed., rev. enl. Casey, J. "Pascal's Theorem." §255 in

64. Euler's Formula use the geometry of its embedding, and some use the threedimensional geometry of the Several of the proofs rely on the Jordan curve theorem, which itself has http://www.ics.uci.edu/~eppstein/junkyard/euler/

Seventeen Proofs of Euler's Formula: V-E+F=2 Many theorems in mathematics are important enough that they have been proved repeatedly in surprisingly many different ways. Examples of this include the existence of infinitely many prime numbers the evaluation of zeta(2) , the fundamental theorem of algebra (polynomials have roots), quadratic reciprocity (a formula for testing whether an arithmetic progression contains a square) and the Pythagorean theorem (which according to Wells has at least 367 proofs). This also sometimes happens for unimportant theorems, such as the fact that in any rectangle dissected into smaller rectangles, if each smaller rectangle has integer width or height, so does the large one. This page lists proofs of the Euler formula: for any convex polyhedron, the number of vertices and faces together is exactly two more than the number of edges. Symbolically V-E+F=2. For instance, a tetrahedron has four vertices, four faces, and six edges; 4-6+4=2. According to Malkevitch , this formula was discovered in around 1750 by Euler , and first proven by Legendre in 1794. Earlier, Descartes (around 1639) discovered a related polyhedral invariant (the total angular defect) but apparently did not notice the Euler formula itself.

65. Interactive Mathematics Miscellany And Puzzles, Geometry Mechanical Proof of the Pythagorean theorem; Extrageometric proofs of the Pythagorean theorem. Pythagorean Triples Java; Quadrilaterals http://www.cut-the-knot.org/geometry.shtml

CTK Exchange Front Page Movie shortcuts Personal info ... Recommend this site Interactive Mathematics Miscellany and Puzzles Geometry Page 3 Utilities Puzzle 4 Travelers problem 9-point Circle as a Locus of Concurrency [Java] A Case of Similarity [Java] A Geometric Limit A problem with equilateral triangles [Java] About a Line and a Triangle [Java] Altitudes [Java] Altitudes and the Euler Line [Java] An Isoperimetric Theorem [Java] Angle Bisectors [Java] Angle Bisectors in a Quadrilateral [Java] Angle Preservation Property [Java] Angle Trisection [Java] Angle Trisectors on Circumcircle [Java] An Old Japanese Theorem Apollonian Gasket [Java] Apollonius Problem [Java] Archimedes' Method Area of Parallelogram [Java] Arithmetic-Geometric Mean Inequality Assimilation Illusion [Java] Asymmetric Propeller [Java] Barbier, The Theorem of [Java] Barycentric coordinates Barycentric coordinates and Geometric Probability Bender: A Visual Illusion [Java] Bisecting arcs Bisecting a shape Bottema's theorem [Java] Bounded Distance Brahmagupta's Theorem [Java] Brianchon's theorem [Java] Bride's Chair [Java] Bulging lines illusion [Java] Butterfly Theorem A Better Butterfly Theorem The Lepidoptera of the Circles [Java] Two Butterflies Theorem [Java] Cantor Set and Function Cantor sets [Java] C - C Cantor's Theorem [Java] Carnot's Theorem Carnot's Theorem Carnot's Theorem (Generalization of Wallace's theorem) [Java] Centroid, a Characteristic Property Of

66. Pappus' Theorem The Duality Principle is a handy feature of Projective geometry you prove one theorem and get another one for free. The principle is quite simple to prove. http://www.cut-the-knot.org/pythagoras/Pappus.shtml

CTK Exchange Front Page Movie shortcuts Personal info ... Recommend this site Pappus' Theorem The word Geometry is of the Greek and Latin origin. In Latin, geo- ge- means earth, while metron is measure. Originally, the subject of Geometry was earth measurement. With time, however, both the subject and the method of geometry have changed. From the time of Euclid's Elements rd century B.C.), Geometry was considered as the epitome of the axiomatic method which itself underwent a fundamental revolution in the 19 th century. Revolutionary in many other aspects, the 19th century also witnessed metamorphosis of a single science - Geometry - into several related disciplines The subject of Projective Geometry , for one, is the incidence of geometric objects : points, lines, planes. Incidence (a point on aline, a line through a point) is preserved by projective transformations, but measurements are not. Thus in Projective Geometry, the notion of measurement is completely avoided, which makes the term - Projective Geometry - an oxymoron. In Projective Geometry

67. Geometry From The Land Of The Incas. Problems, Theorems, Proofs, Quizzes, With A Presents geometry problems, with proofs, animation and sound Poncelet, Napoleon, Eyeball, Steiner, Carnot, Sangaku, Morley, Langley and the Butterfly theorem. http://agutie.homestead.com/files/

Presents geometry problems, with proofs, animation and sound: Poncelet, Napoleon, Eyeball, Steiner, Carnot, Sangaku, Morley, Langley and the Butterfly Theorem. Also, Inca Geometry (Cuzco, Machu Picchu, Incan Quipu, Nazca Lines, Lord of Sipan); quotes from Descartes, Galileo, Newton, Pappus, Plato, Poincare, Voltaire; and quizzes.

68. Discussion The Pythagorean theorem, a cornerstone of Euclidean geometry, is not true. Scale models are impossible, as the size changes, so do the angles. http://cvu.strath.ac.uk/courseware/msc/jgraves/

Non-Euclidean Geometry This tutorial consists of html constructed pages which explain non-Euclidean geometry, and a JAVA constructed applet which demonstrates it visually Development of Euclidean Geometry Description of Euclidean Geometry basic geometry ), and the more complicated ones which relied on axiom 5 in their proof ( Euclidean geometry Problems with Euclidean Geometry Many mathematicians after Euclid (and even Euclid himself) where not comfortable with axiom five, it is quite a complicated statement and axioms are meant to be small, simple and straightforward. Axiom five is more like a theorem than an axiom, and as such it should have to be proved to be true and not assumed. The problem that Euclid and every mathematician after him found for 200 years was that it could not be proven from the 4 axioms before it. However, all the theorems that can be proved from it worked and many mathematicians were happy just to leave it. It is something that seems obviously true and yet was impossible to prove mathematically in a satisfactory way. Development of Hyperbolic Geometry Description of Hyperbolic Geometry Hyperbolic geometry is hard to describe. Its basic premise, that there can be multiple parallel lines through a point, is itself very hard to accept. In purely mathematical terms it is not so difficult. It consists of all Euclid's theorems that can be proved from the first four axioms (

69. PinkMonkey.com Geometry Study Guide - 6.2 The Theorem Of Pythagoras 6.2 The theorem of Pythagoras. Figure 6.3. D ABC is a right triangle. Index. 6.1 The Right Triangle 6.2 The theorem of Pythagoras 6.3 Special Right Triangles. http://www.pinkmonkey.com/studyguides/subjects/geometry/chap6/g0606201.asp

Support the Monkey! Tell All your Friends and Teachers Get Cash for Giving Your Opinions! Get a scholarship! Need help with your research paper? See What's New on the Message Boards today! Favorite Link of the Week. ... Request a New Title Win a $1000 or more Scholarship to college! Place your Banner Ads or Text Links on PinkMonkey for $0.50 CPM or less! Pay by credit card. Same day setup. Please Take our User Survey 6.2 The Theorem of Pythagoras Figure 6.3 D ABC is a right triangle. l (AB) = c l (BC) = a l (CA) = b CD is perpendicular to AB such that D ABC ~ D CBD or l (BC) l (AB) l (CD) a = c x = cx D ABC ~ D ACD or l (AC) l (AB) l (AD) b = c Therefore, from (1) and (2) a + b = cx + cy = c ( x + y ) = c c = c a + b = c The square of the hypotenuse is equal to the sum of the squares of the legs. Converse of Pythagoras Theorem : In a triangle if the square of the longest side is equal to the sum of the squares of the remaining two sides then the longest side is the hypotenuse and the angle opposite to it, is a right angle. Figure 6.4

70. PinkMonkey.com Geometry Study Guide - 5.4 Basic Proportionality Theorem 5.4 Basic Proportionality theorem. If a line is drawn parallel to one side of a triangle and it intersects the other two sides at http://www.pinkmonkey.com/studyguides/subjects/geometry/chap5/g0505401.asp

Support the Monkey! Tell All your Friends and Teachers Get Cash for Giving Your Opinions! Get a scholarship! Need help with your research paper? See What's New on the Message Boards today! Favorite Link of the Week. ... Request a New Title Win a $1000 or more Scholarship to college! Place your Banner Ads or Text Links on PinkMonkey for $0.50 CPM or less! Pay by credit card. Same day setup. Please Take our User Survey Figure 5.4 l paralled to seg.QR. l intersects seg.PQ and seg.PR at S and T respectively. D PTS and D QTS D QTS ) = A ( D SRT ) as they have a common base seg.ST and their heights are same as they are between parallel lines. l which is parallel to seg.QR divides seg.PQ and seg.PR in the same ratio. next page Index 5.1 Introduction 5.2 Ratio And Proportionality ... 5.3 Similar Polygons 5.4 Basic Proportionality Theorem 5.5 Angle Bisector Theorem

71. PlanetMath: Darboux's Theorem (symplectic Geometry) Darboux s theorem (symplectic geometry), (theorem). Attachments proof of Darboux s theorem (symplectic geometry) (Proof) by stlisi. http://planetmath.org/encyclopedia/DarbouxsTheoremSymplecticGeometry.html

(more info) Math for the people, by the people. Encyclopedia Requests Forums Docs ... Random Login create new user name: pass: forget your password? Main Menu sections Encyclop¦dia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Corrections talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information Docs Classification News Legalese ... TODO List Darboux's Theorem (symplectic geometry) (Theorem) If is a -dimensional symplectic manifold , and , then there exists a neighborhood of with a coordinate chart such that These are called canonical or Darboux coordinates . On is the pullback by of the standard symplectic form on , so is a symplectomorphism . Darboux's theorem implies that there are no local invariants in symplectic geometry , unlike in Riemannian geometry, where there is curvature "Darboux's Theorem (symplectic geometry)" is owned by bwebste view preamble View style: HTML with images page images TeX source Attachments: proof of Darboux's Theorem (symplectic geometry) (Proof) by stlisi Cross-references: curvature geometry invariants symplectomorphism ... symplectic manifold This is version 1 of Darboux's Theorem (symplectic geometry) , born on 2002-12-12.

72. Pythagorean Theorem - Wikipedia, The Free Encyclopedia This means that in nonEuclidean geometry, the Pythagorean theorem must necessarily take a different form from the Euclidean theorem. http://en.wikipedia.org/wiki/Pythagorean_theorem

Pythagorean theorem From Wikipedia, the free encyclopedia. In mathematics , the Pythagorean theorem or Pythagoras' theorem , is a relation in Euclidean geometry between the three sides of a right triangle. The theorem is named after and commonly attributed to the 6th century BC Greek philosopher and mathematician Pythagoras , although the facts of the theorem were known by Indian and Greek mathematicians well before he lived. Table of contents 1 The theorem 2 A visual proof 3 The converse 4 Generalisations ... edit The theorem The Pythagorean theorem states: The sum of the areas of the squares on the legs of a right triangle is equal to the area of the square on the hypotenuse. A right triangle is a triangle with one right angle ; the legs are the two sides that make up the right angle, and the hypotenuse is the third side opposite the right angle. In the picture below, a and b are the legs of a right triangle, and c is the hypotenuse: Pythagoras perceived the theorem in this geometric fashion, as a statement about areas of squares: The sum of the areas of the blue and red squares is equal to the area of the purple square.

73. Riemannian Geometry - Wikipedia, The Free Encyclopedia Classical theorems in Riemannian geometry. What Nash embedding theorems also called Fundamental theorem of Riemannian geometry. They http://en.wikipedia.org/wiki/Riemannian_geometry

Riemannian geometry From Wikipedia, the free encyclopedia. In mathematics Riemannian geometry has at least two meanings, one which described in this article and an other also called elliptic geometry In differential geometry Riemannian geometry is the study of smooth manifolds with Riemannian metrics ; i.e. a choice of positive-definite quadratic form on a manifold 's tangent spaces which varies smoothly from point to point. This gives in particular local ideas of angle length of curves , and volume . From those some other global quantities can be derived, by integrating local contributions. It was first put forward in generality by Bernhard Riemann in the nineteenth century . As particular special cases there occur the two standard types ( spherical geometry and hyperbolic geometry ) of Non-Euclidean geometry , as well as Euclidean geometry itself. These are all treated on the same basis, as are a broad range of geometries whose metric properties vary from point to point. Any smooth manifold admits a Riemannian metric and this additional structure often helps to solve problems of differential topology . It also serves as an entry level for the more complicated structure of pseudo-Riemannian manifolds , which (in dimension four) are the main objects of general relativity theory.

74. History Of Geometry In Book VII, he proved Pappus theorem which forms the basis of modern projective geometry; and also proved Guldin s theorem (rediscovered in 1640 by Guldin http://geometryalgorithms.com/history.htm

History Home Overview [History] Algorithms Books Gifts Web Sites A Short History of Geometry Ancient This is a short outline of geometry's history, exemplified by major geometers responsible for it's evolution. Click on a person's picture or name for an expanded biography at the excellent: History of Mathematics Archive (Univ of St Andrews, Scotland) Also, Click these links for recommended: Greek Medieval Modern History Books ... History Web Sites Ancient Geometry (2000 BC - 500 BC) Babylon Egypt The geometry of Babylon (in Mesopotamia) and Egypt was mostly experimentally derived rules used by the engineers of those civilizations. They knew how to compute areas, and even knew the "Pythagorian Theorem" 1000 years before the Greeks (see: Pythagoras's theorem in Babylonian mathematics ). But there is no evidence that they logically deduced geometric facts from basic principles. Nevertheless, they established the framework that inspired Greek geometry. A detailed analysis of Egyptian mathematics is given in the book: Mathematics in the Time of the Pharaohs India (1500 BC - 200 BC) The Sulbasutras Baudhayana (800-740 BC) Apastamba (600-540 BC) Greek Geometry (600 BC - 400 AD) Time Line of Greek Mathematicians Major Greek Geometers (listed cronologically) [click on a name or picture for an expanded biography].

75. Figures And Polygons of the length of the hypotenuse. This is known as the Pythagorean theorem. Examples Example For the right triangle above, the http://www.mathleague.com/help/geometry/polygons.htm

Figures and polygons Polygon Regular polygon Vertex Triangle ... Math Contests School League Competitions Contest Problem Books Challenging, fun math practice Educational Software Comprehensive Learning Tools Visit the Math League Polygon A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others. Examples: The following are examples of polygons: The figure below is not a polygon, since it is not a closed figure: The figure below is not a polygon, since it is not made of line segments: The figure below is not a polygon, since its sides do not intersect in exactly two places each: Regular Polygon A regular polygon is a polygon whose sides are all the same length, and whose angles are all the same. The sum of the angles of a polygon with n sides, where n n - 2) degrees. Examples: The following are examples of regular polygons: Examples: The following are not examples of regular polygons: Vertex 1) The vertex of an angle is the point where the two rays that form the angle intersect. 2) The vertices of a polygon are the points where its sides intersect.

76. Notes On Differential Geometry By B. Csikós translation, symmetric connections, Riemannian manifolds, compatibility with a Riemannian metric, the fundamental theorem of Riemannian geometry, LeviCivita http://www.cs.elte.hu/geometry/csikos/dif/dif.html

Differential Geometry Budapest Semesters in Mathematics Lecture Notes by Balázs Csikós FAQ: How to read these files? Answer: The files below are postscript files compressed with gzip . First decompress them by gunzip , then you can print them on any postscript printer, or you can use ghostview to view them and print selected (or all) pages on any printer. CONTENTS Unit 1. Basic Structures on R n , Length of Curves. Addition of vectors and multiplication by scalars, vector spaces over R, linear combinations, linear independence, basis, dimension, linear and affine linear subspaces, tangent space at a point, tangent bundle; dot product, length of vectors, the standard metric on R n ; balls, open subsets, the standard topology on R n , continuous maps and homeomorphisms; simple arcs and parameterized continuous curves, reparameterization, length of curves, integral formula for differentiable curves, parameterization by arc length. Unit 2. Curvatures of a Curve Convergence of k-planes, the osculating k-plane, curves of general type in R n , the osculating flag, vector fields, moving frames and Frenet frames along a curve, orientation of a vector space, the standard orientation of R n , the distinguished Frenet frame, Gram-Schmidt orthogonalization process, Frenet formulas, curvatures, invariance theorems, curves with prescribed curvatures.

77. 51: Geometry work. Cinderella, featured in the paper Automatic theorem proving of Geometric theorems , H. Crapo and J. RichterGerbert. Downloadable http://www.math.niu.edu/~rusin/known-math/index/51-XX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 51: Geometry Introduction Geometry is studied from many perspectives! This large area includes classical Euclidean geometry and synthetic (non-Euclidean) geometries; analytic geometry; incidence geometries (including projective planes); metric properties (lengths and angles); and combinatorial geometries such as those arising in finite group theory. Many results in this area are basic in either the sense of simple, or useful, or both! There is separate page for constructibility questions (i.e. compass-and-straightedge constructions). There is a separate page for a triangulation problem (in the geographers' sense, not the topologists'). Included on that page is information about determining location by distances from fixed points. History A bibliography (and some related web sites) on the history of geometry is available from David Joyce. See the article on NonEuclidean geometry at St Andrews. Applications and related fields As appealing as questions on simple geometry are, they are often mathematically speaking rather trivial, so we have little material here. Some of the meatier issues in "geometry" are easily classified somewhere else. Thus you'll have to look elsewhere for topics on

78. 53: Differential Geometry curvature is intrinsic); Piecewiselinear versions of Gauss-Bonnet curvature theorem; writhe, linking numbers and applications of differential geometry to the http://www.math.niu.edu/~rusin/known-math/index/53-XX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 53: Differential geometry Introduction Differential geometry is the language of modern physics as well as an area of mathematical delight. Typically, one considers sets which are manifolds (that is, locally resemble Euclidean space) and which come equipped with a measure of distances. In particular, this includes classical studies of the curvature of curves and surfaces. Local questions both apply and help study differential equations; global questions often invoke algebraic topology. History See e.g. Berger, M. "Riemannian geometry during the second half of the twentieth century", Jahresber. Deutsch. Math.-Verein. 100 (1998), no. 2, 45208. CMP1637246 Applications and related fields For differential topology, See 57RXX. For foundational questions of differentiable manifolds, See 58AXX Geometry of spheres is in the sphere FAQ . There is a separate section for detailed information about 52A55: Spherical Geometry A metric in the sense of differential geometry is only loosely related to the idea of a metric on a metric space Subfields Classical differential geometry Local differential geometry Global differential geometry, see also 51H25, 58-XX; for related bundle theory, See 55RXX, 57RXX

79. Spherical Geometry Angles in Spherical geometry. In theorem 1.1 On a sphere of radius R, a triangle with interior angles , , and has area given by First http://www.math.uncc.edu/~droyster/math3181/notes/hyprgeom/node5.html

Next: Logic and the Axiomatic Up: Neutral and Non-Euclidean Geometries Previous: The Origins of Geometry 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 geometrythe study of the Earth, idealized as a sphere. This early science was astronomy and the need to measure time accurately by the sun. We have to come to some agreement on what lines and line segments on a sphere are going to be. A great circle on a sphere is the intersection of that sphere with a plane passing through the center of the sphere. Examples of great circles are the equator and the lines of constant longitude (such as the Greenwich Mean Time Line ). These are good choices to play the role of lines on our sphere. For example, given any two non-antipodal points there is a unique great circle joining those two points. This is easy to see when you remember that three non-collinear points determine a plane. Take these two points and the center of the sphere as the three non-collinear points. The intersection of the plane determined by these points and the sphere is the great circle joining the two given points. If great circles are to be lines, then we can measure the angle between two intersecting great circles as the angle formed by the intersection of the two defining planes with the plane tangent to the sphere at the point of intersection. See the figure below (Figure

80. Mathematics Archives - Topics In Mathematics - Geometry Mathworld geometry ADD. KEYWORDS Definitions, List of theorem; Museo Universitario di Storia Naturale e della Strumentazione Scientifica - Mathematical http://archives.math.utk.edu/topics/geometry.html

Topics in Mathematics Geometry Alice Meets the 4th Dimension ADD. KEYWORDS: Four Dimensional Cube AMS's Materials Organized by Mathematical Subject Classification ADD. KEYWORDS: Electronic Journals, Preprints, Web Sites, Databases AskERIC Lesson Plans - Geometry Border Pattern Gallery ADD. KEYWORDS: Symmetry Cabri Java Project ADD. KEYWORDS: Examples, Animations, 3D geometry, Loci, Conics, Hyperbolic Geometry SOURCE: TECHNOLOGY: Java applets ADD. KEYWORDS: Cabri Geometry resources Cercle d'Euler ADD. KEYWORDS: Euler Circles, Malfatti Circles, Poncelet Triangles, Morley Triangles, Podaires Triangles, Fermat Points, Feuerbach Points, Nagel Points, Gergonne Points Combinatorial Tiling Theory: Theorems - Algorithms - Visualization ADD. KEYWORDS: Two Dimensional Tilings, Three Dimensional Tilings, Face-Transitive Tilings, Periodic Delone Tilings, Orbifold Graphs, Classification of 3-Dimensional Tilings, Tiling Space by Platonic Solids, Enumeration of Polyhedral Crystal Structures The Computation of Certain Numbers Using a Ruler and Compass ADD. KEYWORDS:

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