121. Pi, Phi And Fibonacci Numbers / The Pi Phi Product T his relationship was derived after Oberg noticed an interesting relationship between pi and phi while contemplating geometric questions related to the http://goldennumber.net/pi-phi-fibonacci.htm

The Golden Number from T he Phi Nest™ Home Phi for Neo'phi'tes Fibonacci Series Golden Sectio ... s You can help support this site by visiting these affiliates: Save on books and other purchases at Amazon Great prices and service on hosting that pays you back Investors: Apply Phi and Fibonacci principles to the stock market Get the benefits of nature's most nutrient-packed foods into your daily diet. Pi, Phi and Fibonacci Numbers p and Fibonacci numbers can be related in several ways: Phi ) and pi p share a common irrational factor T he two most famous numbers in the history of mathematics p are exactly related to each other by a rational fraction , even though both are irrational numbers. Roger Logan in his paper entitled THE MAGNIFICENT PERFECT SQUARE © 2001 introduc es the concept that both and p are composite numbers sharing a common irrational factor . When put in the form of a fraction, p , this common irrational factor cancel s out

122. What Is GHL? A library for 2D and 3-D geometric calculation in C, with functions for shape generation, geometric evaluation, intersection, and offsetting and filleting. http://www.pml.co.jp/ghl/index.html

Geometry Handling Library Japanese Contents What is GHL? Release Notes More Details Demo Version ... GHL Users What is GHL? This is a complete C functions library of 2-D and 3-D geometric calculation. The library includes functions which calculate the following items for analytical and free-formed shapes, including NURBS, with high reliability and precision. Shape generation Evaluation of generated geometric elements Intersection of any combination of analytical and free-formed shapes Offsetting and filleting (2-D and 3-D) More than 2,000 external routines are included in this library. This library is written in standard C language, and thus portable to most of the workstations and personal computers working under various operating sysytems as follows. SGI IRIX Sun Solaris HP HP-UX Various PC Unixes Apple Mac OS X This product is used by various application systems which require precise geometric operations from 1992. GHL will be revised continuously to incorporate newly developed theory and algorithms. GHL 3.4.7 : latest version (shipped on Nov. '03 GHL 3.4.7 Release Note

123. Geometry Around Black Holes A WWW Exhibition in Relativistic Computer Dynamics and Visualization http://www.astro.ku.dk/~cramer/RelViz/

Award June 10th 1997 Award July 7th 2000 'Highly Rated by Schoolzone' Cramer's Homepage Geometry Around Black Holes A WWW Exhibition in Relativistic Computer Dynamics and Visualization By Michael Cramer Andersen, June 1996. Contents of this WWW Visualization Exhibition: General Relativity and Black Holes. Curvature and lightcones. Kerr's rotating Black Holes. Gravitational redshift. ... Other sites with black holes... You are guest no. Updated June 18th 1997 by cramer@astro.ku.dk . Links to this site: http://www.astro.ku.dk/~cramer/RelViz/

124. Nineteenth Century Geometry By Roberto Torretti, Universidad de Chile. http://plato.stanford.edu/entries/geometry-19th/

version history HOW TO CITE THIS ENTRY Stanford Encyclopedia of Philosophy A B C D ... Z This document uses XHTML-1/Unicode to format the display. Older browsers and/or operating systems may not display the formatting correctly. last substantive content change MAR Nineteenth Century Geometry 1. Lobachevskian geometry 2. Projective geometry 3. Klein's Erlangen program 4. Axiomatics perfected ... Related Entries 1. Lobachevskian geometry Euclid (fl. 300 b.c.) placed at the head of his Elements aitemata 1. To draw a straight line from any point to any point. 3. To draw a circle with any center and any radius. Figure 1 In the darker ages that followed, Euclid's sense of mathematical freedom was lost and philosophers and mathematicians expected geometry to rest on self-evident grounds. Now, if a is perpendicular and b is almost perpendicular to PQ, a and b approach each other very slowly on one side of PQ and it is not self-evident that they must eventually meet somewhere on that side. After all, the hyperbole indefinitely approaches its asymptotes and yet, demonstrably, never meets them. Through the centuries, several authors demanded-and attempted-a proof of Euclid's Postulate. John Wallis (b. 1616, d. 1703) derived it from the assumption that there are polygons of different sizes that have the same shape. But then this assumption needs proof in turn. Girolamo Saccheri (b. 1667, d. 1733) tried reductio . He inferred a long series of propositions from the negation of Euclid's Postulate, until he reached one which he pronounced "repugnant to the nature of the straight line". But Saccheri's understanding of this "nature" was nourished by Euclidean geometry and his conclusion begged the question.

125. The Geometry Junkyard: Knot Theory A page of links on geometric questions arising from knot embeddings. http://www.ics.uci.edu/~eppstein/junkyard/knot.html

Knot Theory There is of course an enormous body of work on knot invariants, the 3-manifold topology of knot complements , connections between knot theory and statistical mechanics, etc. I am instead interested here primarily in geometric questions arising from knot embeddings. Animated 3d curves and knots , Jos Leys. Atlas of oriented knots and links , Corinne Cerf extends previous lists of all small knots and links, to allow each component of the link to be marked by an orientation. Borromean rings don't exist . Geoff Mess relates a proof that the Borromean ring configuration (in which three loops are tangled together but no pair is linked) can not be formed out of circles. Dan Asimov discusses some related higher dimensional questions. Matthew Cook conjectures the converse Are Borromean links so rare? S. Javan relates the history of the links and describes various generalizations with more than three rings. For more history and symbolism of the Borromean rings, see Peter Cromwell's web site . See also Paul Bourke's Borromean rings page A Brunnian link . Cutting any one of five links allows the remaining four to be disconnected from each other, so this is in some sense a generalization of the Borromean rings. However since each pair of links crosses four times, it can't be drawn with circles.

126. Amnon Besser: Homepage Ben Gurion University. Number theory, algebraic cycles, algebraic Ktheory and arithmetic geometry. Research, publications, course information, and links. http://www.cs.bgu.ac.il/~bessera/

Dr. Amnon Besser Address Department of Mathematics Ben Gurion University Be'er Sheva 84105 Israel Phone Fax E-mail: bessera@math.bgu.ac.il Room NO. Office hours : Monday 14-16 Education B.Sc. : Tel Aviv University 1985 M.Sc. : Tel Aviv University 1987 Ph.D. : Tel Aviv University 1993 Research Research Interests: Number theory, Arithmetic geometry, p-adic integration, p-adic cohomology, Shimura varieties, Automorphic forms, Algebraic cycles, Algebraic K-theory. List of publications from mathscinet (requires mathscinet authorization) Research profile Research Group: Number Theory and Algebraic Geometry Postdoctoral positions in the group Number theory and Algebraic geometry seminar Publications On the measure of large trigonometric sums , Astererisque 258 (1999) 35-76 CM cycles over Shimura Curves , Journal of Algebraic geometry 4 (1995) 659-691 Elliptic fibrations of K3 surfaces and QM kummer surfaces , Math. Zeitschrift 228 (1998), No. 2, 283-308 On the Kolyvagin cup product , Transactions of the Amer. Math. Soc. 349 (1997), No. 11, 4635-4657 , Doc. Math. 2 (1997), No. 02, 31-46 (electronic)

127. Veys University of Leuven. Algebraic geometry, singularity theory, applications in number theory. Papers and preprints. http://www.wis.kuleuven.ac.be/algebra/veys.htm

Home Page of Wim Veys Contents Work Information Contact Information Publications with available DVI- and PS-file Previous publications Work Information Professor at the University of Leuven (K.U.Leuven), Department of Mathematics, Section of Algebra Fields of Research Algebraic Geometry, Singularity Theory, applications in Number Theory Specific Research Topics Exceptional divisor of an embedded resolution, Zeta Functions (Igusa, topological, motivic), Monodromy, configurations of curves on surfaces, Stringy invariants, Principal value integrals Ph.D. Students Bart Rodrigues : Geometric determination of the poles of motivic and topological zeta functions may 2002 Dirk Segers : Smallest poles of zeta functions and solutions of polynomial congruences, april 2004 Jan Schepers : On stringy invariants Ann Lemahieu : On possible poles of zeta functions Filip Cools Back to top Contact Information Address University of Leuven, Department of Mathematics, Celestijnenlaan 200 B, B-3001 Leuven (Heverlee), Belgium. Electronic mail address wim.veys@wis.kuleuven.ac.be

128. Pi, Star Of Bethlehem Magi Astronomy Astrology Archaeology Both pi discoveries incorporate transpositions of pi from a geometric ratio to time. . . The pi of Time. Conversion of Egyptian http://www.aloha.net/~johnboy/pi.htg/pi.htm

a n d t h e P i F a c t o r "The Great Pyramid is also a "sculpture" of a photon "at rest" and its secret Pi dimension leads to The Star of Bethlehem - The Capstone of The Great Pyramid a Unified Field Theory and the source of a "week" as a measurement of time Star of Bethlehem Sitemap "God is The Great Geometer" - Plato The Circumference of the universe is Pi A Unified Field Theory Theorem One If the diameter of the universe is "1 universe" then the circumference of the universe is Pi (Circumference = Pi D) Theorem Two If the circumference of the universe is Pi (written as a number) then the universe is infinite* Theorem Three If the universe is infinite then every point is the center of the universe *"Pi" is used here as a "transcendental number" which does not represent a quantifiable measurement. Transcendental Pi represents a "symbol of the universe" because both Pi and the universe contain infinite "strings" of non-repeating patterns which produce no two "things" (significant sequences) that are virtually identical. "The universe e x p a n d s or contracts depending upon the availability of grant money".

129. Topology And Geometry A collection of educational, graphical and research software by Jeff Weeks. http://www.geometrygames.org/

Jeff Weeks' Topology and Geometry Software Fun and Games for ages 10 and up Torus and Klein Bottle games (online) Kali (Windows, Macintosh) KaleidoTile (Windows, Macintosh) Classroom Materials for teachers grades 6-10 Exploring the Shape of Space Curved Spaces for software developers Computer Graphics in Curved Spaces (OpenGL, Direct3D) Research Software for mathematicians SnapPea (Linux, Macintosh, Windows) Comments? Problems? Suggestions? Contact Jeff Weeks awards and links

130. Graphics Group Conducts research in realtime 3D model aquisition, shape-based retrieval and analysis, video mosaics, lapped textures, texture mapping for cel animation, and algorithm animation. http://www.cs.princeton.edu/gfx/

Princeton CS Dept Local Access Princeton CS Dept Local Access

131. An Invitation To Arithmetic Geometry Dino Lorenzini. Additions, corrections, review, preface. http://www.math.uga.edu/~lorenz/book.html

An Invitation to Arithmetic Geometry Professor Kleinert reviews the book in Zentralblatt fur Mathematik and writes: ...an extremely carefully written, masterfully thought out, and skil[l]fully arranged introduction and quite so an invitation, as promised to the arithmetic of algebraic curves, on the one hand, and to the algebro-geometric aspects of number theory, on the other hand. Detailed discussions, full proofs, much effort at thorough motivations, a wealth of illustrating examples, numerous related exercises and problems, hints for further reading, and a rich bibliography characterize this text as an excellent guide for beginners in arithmetic geometry... a highly welcome addition to the existing literature. The book was developed from the notes of a year-long course taught at UGA. It is intended for upper level undergraduates and graduate students. The reviewer in Zentralblatt stresses the innovation in Professor Lorenzini's ``quite unconventional way'' of teaching arithmetic geometry. The text... does justice to its author's method[olog]ical intentions in a very remarkable and, what is more, nearly perfect manner,... a method[olog]ical inspiration for teachers of the subject.

132. Hyperbolic Geometry Cabri constructions for the demonstration of the basic concepts of hyperbolic geometry in the Poincare disc model. http://mcs.open.ac.uk/tcl2/nonE/nonE.html

Hyperbolic Geometry using Cabri This page and links maintained by Tim Lister, t.c.lister@open.ac.uk Last updated: A tessellation of the hyperbolic plane H Full screen version of diagram During the summer of 97 I had great fun playing with some marvelous software, Cabri Geometry , and devising constructions for use in teaching the basic ideas of a geometry course put on by the Open University. These started with some figures to demonstrate the transformations of Inversive Geometry, and progressed to figures for the Arbelos, the inversors of Peucellier and Hart, Coaxial Circles and so on, much of which was driven by the discovery of a Dover edition of a small pearl of a book Advanced Euclidean Geometry (Modern Geometry) An elementary Treatise on the Geometry of the triangle and the Circle (to give its full title) written by Roger A. Johnson and first published in 1929. It had languished on my bookshelves, having been bought years ago for 20 cents (South African) in some sale or other. I can recommend it as a fascinating read, or just for taking in the breathtaking complexity of the many hand crafted diagrams to be found on its pages.

133. Diophantine Geometry GeorgAugust-Universit¤t, G¶ttingen, Germany; 1722 June 2004. http://www.uni-math.gwdg.de/yuri/SS04/conference.html

<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> Conference "Diophantine Geometry Mathematisches Institut Organizer: Yuri Tschinkel Program Useful information Contact us Short Courses: J.-B. Bost , (Orsay): Foliations on algebraic varieties over number fields: algebraicity and transcendence B. Hassett , (Rice University): Equations of universal torsors and Cox rings R. Pink Special points and subvarieties of abelian varieties Other participants include: V. Abrashkin , (University of Durham) V. Batyrev

134. Notes On Differential Geometry By B. Csikós Notes by Bal¡zs Csik³s. Chapters in PostScript. 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.

135. [gr-qc/9911051] Complex Geometry Of Nature And General Relativity A paper by Giampiero Esposito attempting to give a selfcontained introduction to holomorphic ideas in general relativity. The main topics are complex manifolds, spinor and twistor methods, heaven spaces. http://arxiv.org/abs/gr-qc/9911051

General Relativity and Quantum Cosmology, abstract gr-qc/9911051 From: [ view email ] Date: Mon, 15 Nov 1999 11:06:50 GMT (124kb) Complex Geometry of Nature and General Relativity Author: Giampiero Esposito Comments: 229 pages, plain Tex Report-no: DSF preprint 99/38 An attempt is made of giving a self-contained introduction to holomorphic ideas in general relativity, following work over the last thirty years by several authors. The main topics are complex manifolds, spinor and twistor methods, heaven spaces. Full-text: PostScript PDF , or Other formats References and citations for this submission: SLAC-SPIRES HEP (refers to , cited by , arXiv reformatted); CiteBase (autonomous citation navigation and analysis) Which authors of this paper are endorsers? Links to: arXiv gr-qc find abs

136. Geometry Of Sri Yantra Artistic and Historical Background. Historical Methods of Duplication. Modern Experiments in Construction. http://alumni.cse.ucsc.edu/~mikel/sriyantra/sriyantra.html

Artistic and Historical Background A curiosity: The mathematics of sriyantra by Joseph The geometry of Sri-yantra by Bolton and Macleod Art of Sri Yantra A connection with Indian ragas by Mookerjee Historical Methods of Duplication Construction by Order of Destruction Construction by Order of Creation Modern Experiments in Construction Construction by Checkerboard Construction by Golden Angle Complexity Measure A note on Computational Complexity of Sri Yantra by Kulaichev Bibliography Links please send your feedback to "mikel_maron [at] yahoo [dot] com"

137. Dipartimento Di Matematica Applicata G. Sansone Editors' page. http://www.jgp.unifi.it/

138. Mathematik.com Individual pages on different topics in Mathematics. Examples group theory, dynamical systems theory, geometry or number theory. http://www.mathematik.com/

Mathematik.com Gradus Suavitatis Turing Billiard Bifurcation ... Feedback

139. Interesting Facts About Pi Interesting Facts about pi. You should circle. The name of this constant is pi and its value is close to 3.1415926535897932 The http://www.arcytech.org/java/pi/facts.html

Interesting Facts about Pi You should have noticed that the ratios for all the circles are very close. The values that you should have gotten should be very close to 3.1. The measurements that you did were not that precise. If they had been, then all of the ratios would be extremely close to each other. What that tells us is that there is a fundamental constant that works with every single circle . The name of this constant is pi and its value is close to ... The Greek letter is used to represent this important constant. Click here to see with five hundred digits of precision. One more thing that you may want to do with your data is get the mean or average of all the ratios (or approximations of ) that you measured to see how close you are to the value of in the previous paragraph. In the rest of this page we have a few interesting facts about , a fundamental constant of nature, is one of the most famous and most remarkable numbers you have ever met. The Egyptians and the Babylonians are the first cultures that discovered about 4,000 years ago. Here is a small table that shows some of the very old discoveries of

140. Mathsforkids | A Scientific Web Site For Kids This site has been created to have fun and to practice maths. Includes addition, substraction, multiplication, geometry. http://www.mathsforkids.com/

Welcome in our web site. This site has been create to have fun and to practice maths. Our mission This site is free. Our mission is strictly educationnal and we always appreciate to receive your comments and suggestions by contacting us via our web site. How it works? The subjects appear in the left column. Select your choice and click on the corresponding blue button.

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