121. Pi Land Fun activities, a pi trivia game and a Trainer for digit memorization. pi poetry,artwork, and photography, calculations, digits and book reviews. http://www.eveandersson.com/pi/

Pi Land Fun Activities: The Pi Trivia Game Pi Trainer Aesthetics: Poetry Photos Art Quotes Nerd Stuff: Frequency of Each Digit of Pi Calculation of Pi Using the Gregory-Leibniz Series Calculation of Pi Using the Monte Carlo Method Digits ... Eve Andersson (eve@eveandersson.com) Comments Pi page Just to say it's wonderful to find the Pi Page still going - as a young(ish) graduate in the early 1990s, the site probably did more than anything else to convince me that Mosaic (ask your grandparents) was useful for something other than downloading porn and spreading maliciously doctored photos worldwide. If there's ever an Internet Lifetime Achievement Award, I'll happily nominate Eve... And another thing - how come nowhere on this page can I find my favourite property of pi, our old friend e^(i*pi)-1? And another thing (part 2) - I just want to point out that I got 13/25 on the Pi Test - and am a qualified mathematician (who admittedly graduated 13 years ago but even so!) And (one last) thing - if the page needs a pompous slogan it should really be "One measures a circle beginning anywhere" (motto of the Fortean Society and all its spin-offs) - it may be meaningless but it sounds very impressive. Which in itself kinda sums up most mathematics. Aidan Merritt Updates Your Pi memorization and calculation records aren't up to date. I knew which records you were talking about, but I think that you should add the fact that 1.2411 trillion digits of pi have been calculated and that the Japanese guy has now memorized 60,000. Other than this you're site is great and I love the trivia game, thx.

122. 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/

123. Alina Carmen Cojocaru Princeton. Arithmetic geometry with techniques from analytic number theory. Preprints and other links. http://www.math.princeton.edu/~cojocaru/

Math research Math teaching Number theory links Other links ... Photos Dr. ALINA-CARMEN COJOCARU Princeton University Mathematics Department 810 Fine Hall, Washington Road Princeton, NJ 08544-1000 USA Phone: (office) (609) 258-5803 Fax: (609) 258-1367 cojocaru at math.princeton.edu

124. The 'Phinest' Source To The Golden Section, Golden Mean, Divine Proportion, Fibo The Golden Section, Ratio or Mean, Geometric construction of phi in the goldensection and pi, Phi Fibo s Powers of Phi Stock Markets Affliates http://goldennumber.net/

GoldenNumber.net Home Contact Meet the Phi Guy "Phriends" in Phi Site Search ... News Dedicated to providing you with the phinest information on The Golden Section , Ratio or Mean The Divine Proportion The Fibonacci Series and the golden number, Phi ( NEW PhiMatrix Graphic Design Software Free Download Site Sections: Overview Design/Composition Life Mathematics ... Other Resources Welcome to GoldenNumber.Net - The Phi Source GoldenNumber.Net exists to share information on the pervasive appearance of Phi in life and the universe. Its goal is to present a broad sampling of phi related topics in an engaging and easy-to-understand format and to provide an online community (aka The Phi Nest), in which new findings about Phi can be shared. Select an area of interest below or START HERE . Enjoy the 'phi nomenon'! SITE CONTENTS Overview Design/Composition Life Mathematics ... Universe News: The Da Vinci Code Dan Brown's book "

125. Behavior Modeler GrafiCalc allows users to simulate and solve a wide range of geometry based computational challenges. http://www.graficalc.com/

126. 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

127. Richard Taylor's Home Page Harvard. Arithmetic algebraic geometry, automorphic forms. Preprints. http://abel.math.harvard.edu/~rtaylor/

R I C H A R D T A Y L O R Here are some recent papers. They are available either as dvi or as postscript files. They may be very slightly different from the published versions, e.g. they may not include corrections made to the proofs. Ihara's lemma and potential automorphy. M.Harris, N.Shepherd-Barron and R.Taylor preprint. dvi Postscript Automorphy for some l-adic lifts of automorphic mod l representations. L.Clozel, M.Harris and R.Taylor preprint. dvi Postscript Compatibility of local and global Langlands correspondences. R.Taylor and T.Yoshida preprint. dvi Postscript Galois representations. (Review article.) R.Taylor Proceedings of ICM 2002, volume I, 449-474. dvi Postscript Galois representations. (Long version of above review article.) R.Taylor Annales de la Faculte des Sciences de Toulouse 13 (2004), 73-119. dvi Postscript Galois representations. R.Taylor slides for talk at ICM 2002. dvi Postscript On the meromorphic continuation of degree two L-functions. R.Taylor

128. Homepage Of EPAG 2001 Topics Spectral theory, index theory, heat equation and other parabolic equation methods, existence and regularity of solutions to elliptic/parabolic equations, geometric and spectral invariants. Potsdam, Germany; 2024 August 2001. http://epag2001.math.uni-potsdam.de/

129. Home Page For Neil Dummigan University of Sheffield. Arithmetical algebraic geometry. Publications. http://www.shef.ac.uk/personal/n/neildummiganshomepage/

Neil Dummigan's home page Contact details Department of Pure Mathematics, Hicks Building, University of Sheffield, Sheffield S3 7RH, U.K. Telephone: +44 114 2223713 Fax: +44 114 2223769 E-mail: n.p.dummigan@sheffield.ac.uk Teaching I am a lecturer in the Department of Pure Mathematics at the University of Sheffield In Autumn 2005-6 I will lecture SOM202 Advanced Calculus. In Spring 2005-6 I will lecture SOM111 Practical Calculus. I am PM Level 2 Tutor and SoMaS Social Sciences Dual Degree Coordinator. Research My field of research is algebraic number theory/arithmetic geometry. Here are some of my recent publications and preprints. I am an editorial advisor for the LMS Journal of Computation and Mathematics. General information for prospective graduate students. Links MathSciNet London Mathematical Society American Mathematical Society UK maths departments ... Penn State , list of mathematical websites around the world, including departments in other countries. Maths Careers website John Cremona's home page, linking to elliptic curve data. William Stein's modular forms database. Keith Matthews's Number Theory web ... Google Neil Dummigan, July 26th, 2005.

130. 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 ... Z This document uses XHTML/Unicode to format the display. If you think special symbols are not displaying correctly, see our guide Displaying Special Characters last substantive content change MAR The Encyclopedia Now Needs Your Support Please Read How You Can Help Keep the Encyclopedia Free 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

131. 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 Borromean paper clips 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.

132. Multimedia Documents At The Geometry Center Research papers, conference proceedings, expository and educational articles. http://www.geom.uiuc.edu/docs/

Register: Tell Us What You Think Up: The Geometry Center Home Page Multimedia Documents: Conference Proceedings The Proceedings of the Conference on Electronic Communication in Mathematics, held May 29 - June 1, 1997 at the Geometry Center, are available online. In keeping with the spirit of the conference, the proceedings consist entirely of electronic documents, together with RealAudio sound recordings of the invited addresses. Research Papers Scientific papers written at the Geometry Center that use the unique aspects of hypertext to present information in a non-linear fashion. Many of these include movies or interactive pictures. Expository Papers Documents written at the Geometry Center that take advantage of hypertext to present information about mathematics or the Geometry Center in a style accessible to a wide audience. Educational Materials Classroom and laboratory materials available electronically from the Geometry Center. Geometry Forum Articles written for the Geometry Forum, a collection of newsgroups that are concerned with geometry and education. Many of these articles describe the mathematics and activities of visitors to the Geometry Center. Geometry Center Preprint Series A collection of online preprints generated with Center support.

133. Homepage: Susanne Schmitt (Max-Planck-Institut Für Informatik) MaxPlanck-Institut f¼r Informatik. Effective computational geometry, separation bounds; Computer algebra; Algebraic number theory, elliptic curves. Publications. http://www.mpi-sb.mpg.de/~sschmitt/

Department 1: Algorithms and Complexity max planck institut informatik Homepage Susanne Schmitt Department 1: Algorithms and Complexity Building 46.1 , Room 318 Stuhlsatzenhausweg 85 Germany Email: Get my email address via email Phone: Fax: Research Interests Real algebraic numbers, Root isolation, Separation bounds Effective Computational Geometry Computer Algebra Algebraic number theory, Elliptic curves Publications Publications of Dr. Susanne Schmitt Teaching Summer term 2005: Seminar Geometrische Algorithmen, Dr. Susanne Schmitt, Dr. Nicola Wolpert Earlier terms Winter term 2004/2005: Seminar Geometric Rounding, Dr. Lutz Kettner, Dr. Susanne Schmitt Winter term 2004/2005: Lecture Dr. Lutz Kettner, Dr. Susanne Schmitt, Dr. Nicola Wolpert Summer term 2004: Seminar Theorie und Praxis geometrischer Algorithmen, Dr. Susanne Schmitt, Dr. Nicola Wolpert Winter term 2003/2004: Lecture Effective Computational Geometry for Curves and Surfaces, Dr. Lutz Kettner, Dr. Susanne Schmitt, Dr. Nicola Wolpert

134. 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

135. 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

136. Pi -- From MathWorld 9293) gives a geometric construction for 3+16/1133.1415929. Landen,Ramanujan, and Arithmetic-Geometric Mean, Ellipses, pi , and the Ladies Diary. http://mathworld.wolfram.com/Pi.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team MATHWORLD - IN PRINT Order book from Amazon Number Theory Constants Pi ... Pi Pi A real number denoted which is defined as the ratio of a circle 's circumference to its diameter It is equal to (Sloane's Pi's digits have many interesting properties, although not very much is known about their analytic properties. Spigot (Rabinowitz and Wagon 1995; Arndt and Haenel 2001; Borwein and Bailey 2003, pp. 140-141) and digit-extraction algorithms (the BBP formula ) are known for Pi's continued fraction is given by [3, 7, 15, 1, 292, 1, 1, 1, ...] (Sloane's ). Its Engel expansion is 1, 1, 1, 8, 8, 17, 19, 300, 1991, 2492, ... (Sloane's is known to be irrational Legendre also proved that is irrational (Wells 1986, p. 76). is also transcendental (Lindemann 1882). An immediate consequence of Lindemann's proof of the transcendence of also proved that the geometric problem of antiquity known as circle squaring is impossible. A simplified, but still difficult, version of Lindemann's proof is given by Klein (1955).

137. The Geometry Junkyard: Polyominoes Numerous links, sorted alphabetically. http://www.ics.uci.edu/~eppstein/junkyard/polyomino.html

Polyominoes and Other Animals Connected subsets of the square lattice tiling of the plane are called polyominoes . These are often classified by their number of squares, so e.g. a tetromino has four squares and a pentomino has five; this nomenclature is by analogy to the word "domino" (a shape formed by two connected squares, but unrelated in etymology to the roots for "two" or "square"). If a polyomino or a higher-dimensional collection of cubes forms a shape topologically equivalent to a ball, it is called an animal . A famous open problem asks whether any animal in three dimensions can be transformed into a single cube by adding and removing cubes, at each step remaining an animal (it is known that removal alone does not always work). Other related figures include polyiamonds (collections of equilateral triangles), polyabolos (collections of half-squares), and polyhexes (collections of regular hexagons). Anna's pentomino page . Anna Gardberg makes pentominoes out of sculpey and agate. Arranging six squares . This Geometry Forum problem of the week asks for the number of different hexominoes, and for how many of them can be folded into a cube. NebulaSearch: Polyomino Blocking polyominos . R. M. Kurchan asks, for each k, what is the smallest polyomino such that k copies can form a "blocked" configuration in which no piece can be slid free of the others, but in which any subconfiguration is not blocked.

138. 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.

139. Hilbert 10 Workshop on Hilbert's 10th problem. University of Gent, Belgium; 25 November 1999. Abstracts. http://cage.rug.ac.be/~hilbrt10/hilbert10.html

Workshop Hilbert's 10th problem, Relations with Arithmetic and Algebraic Geometry University of Gent, November 2-5 Het Pand Organisers: G. Cornelissen, J. Denef, A. Herremans, K. Hoornaert, L.Lipshitz, T. Pheidas, J. Van Geel, K. Zahidi Scientific committee: J. Denef, L.Lipshitz, T. Pheidas, J. Van Geel The organisation of this workshop is supported by the FWO and the FWO Research network WO.011.96N The main theme of the meeting The lectures Speakers and titles (abstracts) The Proceedings ... The Participants The main theme of the meeting was the relation between decidability problems, arithmetic and algebraic geometry. There were series of lectures with an instructional character with the following topics: Back to contents Work on Hilbert's 10th problem, for various rings and fields, over the past decades. Some model theoretic aspects and related decidability problems. Decidability for certain generic diophantine problems and for fragments of arithmetic. The algebraic geometric structure of Diophantine families. Mazur's conjectures on the topology of rational points. Computational aspects. Work of Rojas on (un)computability of bounds for integral points on curves and Diophantine sentences in four variables.

140. The Nature Of Pi The Nature of pi objects have shape and size. Objects of the same shape aresimilar. Circles are geometric figures of a certain (circular) shape. http://www.cut-the-knot.org/pythagoras/NatureOfPi.shtml

Username: Password: Sites for teachers Sites for parents Awards Interactive Activities ... Sites for parents Also he hath demonstrated the proportion of the Diameter to the Circumference and shews what was the reason why Archimedes did use these two numbers ... John Aubrey Brief Lives , Penguin Books, 2000, p. 378 Determination of p Introduction The customary game plan for determination of p that tabulates measurements of several circular objects appears to simultaneously serve two ends: establishing existence of p and approximating its value. Both goals are better served by other means. In the framework of similarity, existence of p is self-evident. Since all circles are similar, their relative (or shape ) attributes are the same for every circle. Approximation of p , too, does not require several objects. p could as well be approximated by taking measurements of a single circular object with different tools and different technics. The Fundamentals Objects around us have shape and size . Two objects of the same shape are similar . If, in addition, they have the same size, they are

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