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Geometry Theorem:     more books (102)

Comparison Theorems in Riemannian Geometry (AMS Chelsea Publishing) by Jeff Cheeger and David G. Ebin, 2008-08-04 18 Theorems of Geometry: for High School Students by William Smith, 2010-06-25 Geometry: Theorems and Constructions by Allan Berele, Jerry Goldman, 2000-10-16 Fermat's Last Theorem for Amateurs by Paulo Ribenboim, 1999-02-11 A Combination of Geometry Theorem Proving and Nonstandard Analysis with Application to Newton's Principia (Distinguished Dissertations) by Jacques Fleuriot, 2001-06-27 Mechanical Geometry Theorem Proving (Mathematics and Its Applications) by Shang-Ching Chou, 2001-11-30 The L²-Moduli Space and a Vanishing Theorem for Donaldson Polynomial Invariants (Monographs in Geometry and Topology, Vol II) by John Willard Morgan, Tomasz Mrowka, et all 1994-06 Stability Theorems in Geometry and Analysis (Mathematics and Its Applications) by Yu.G. Reshetnyak, 2010-11-02 Mechanical Theorem Proving in Geometries: Basic Principles (Texts and Monographs in Symbolic Computation) by Went Sun Wu, Xiao Fan Jin, et all 1994-05 Machine Proofs in Geometry: Automated Production of Readable Proofs for Geometry Theorems (Series on Applied Mathematics) by Shang-Ching Chou, Xian-Shan Gao, et all 1994-04 Fermat's Last Theorem: A Genetic Introduction to Algebraic Number Theory (Graduate Texts in Mathematics) by Harold M. Edwards, 2000-01-14 An Introduction to the Geometry of Numbers (Classics in Mathematics) by J.W.S. Cassels, 1997-02-25 Mathematics Mechanization: Mechanical Geometry Theorem-Proving, Mechanical Geometry Problem-Solving and Polynomial Equations-Solving (Mathematics and Its Applications) by Wu Wen-tsun, 2001-04-30 Principles and Problems of Plane Geometry with Coordinate Geometry (Includes 850 Solved in Detail Problems) [Schaum's Outline Series] by Barnett Rich, 1963

lists with details

1. 2. GEO - A Collection Of Mechanized Geometry Theorem Proofs
   next up previous Next 5. The Current State Up 4. Two Examples Previous 1.INTPS a 2. GEO - a collection of mechanized geometry theorem proofs.  
   http://www.mathematik.uni-kl.de/~zca/Reports_on_ca/27/paper_html/node11.html
   
   Extractions: Next: 5. The Current State Up: 4. Two Examples Previous: 1. INTPS - a As a second application of our general framework we collected examples from mechanized geometry theorem proving scattered over several papers mainly of W.-T. Wu, D. Wang, and S.-C. Chou, but also from other sources. The corresponding GEO table contains about 250 records of examples, most of them considered in Chou's elaborated book [ The examples collected so far are related to the coordinate method as driving engine as described in [ ]. The automated proofs may be classified as constructive (yielding rational expressions to be checked for zero equivalence) or equational (yielding a system of polynomials as premise and one or several polynomials as conclusion). To distinguish between the different problem classes we defined a mandatory tag prooftype that must be one of several alternations defined in the Syntax attribute in the corresponding meta sd-file. Extending/modifying this entry modifies the set of valid proof types. Hence the table is open also for new or refined approaches. According to the general theory, see, e.g., [

2. Projective Geometry Theorem
   a topic from geometrycollege. Projective geometry theorem  
   http://mathforum.com/epigone/geometry-college/brandwehsal

3. GEOTHER - Geometry Theorem Prover
   GEOTHER (geometry theorem provER) is an environment implemented by Dongming Wangin Maple with drawing routines and interface written previously in C and now  
   http://calfor.lip6.fr/~wang/GEOTHER/
   
   Extractions: GEOTHER (GEOmetry THeorem provER) is an environment implemented by Dongming Wang in Maple with drawing routines and interface written previously in C and now in Java for manipulating and proving geometric theorems. In GEOTHER a theorem is specified by means of predicates of the form Theorem(H,C,X) asserting that H implies C , where H and C are lists or sets of predicates that correspond to the geometric hypotheses and the conclusion of the theorem, and the optional X is a list of variables for the internal computation. The information contained in the specification may be all that is needed in order to manipulate and prove the theorem. From the specification, GEOTHER can automatically assign coordinates to each point in some optimal manner; translate the predicate representation of the theorem into an English statement, into a first-order logical formula, or into algebraic expressions; draw one or several diagrams for the theorem - the drawn diagrams may be animated, modified, and saved as PostScript files; prove the theorem using any of the six algebraic provers;

4. New(?) Geometry Theorem
   a topic from geometrycollege. new(?) geometry theorem  
   http://mathforum.com/epigone/geometry-college/bendskangdwex

5. Enumerative Real Algebraic Geometry: Theorem 4.4
   4.ii.c. Proof of Theorem 4.4. Theorem 4.6 (So9, Theorem 4.2) Let L be areal real (nk)-plane, none of whose Plücker coordinates vanishes.  
   http://www.math.umass.edu/~sottile/pages/ERAG/S4/2.3.html

6. KLUWER Academic Publishers | Mechanical Geometry Theorem Proving
   Books » Mechanical geometry theorem Proving. Mechanical geometry theoremProving. Kluwer Academic Publishers is pleased to make this  
   http://www.wkap.nl/prod/b/1-4020-0330-7

7. KLUWER Academic Publishers | Mathematics Mechanization
   Mathematics Mechanization Mechanical geometry theoremProving, MechanicalGeometry Problem-Solving and Polynomial Equations-Solving. Add to cart.  
   http://www.wkap.nl/prod/b/0-7923-5835-X
   
   Extractions: The book is divided into three parts. Part I concerns historical developments of mathematics mechanization, especially in ancient China. Part II describes the underlying principles of polynomial equation-solving, with polynomial coefficients in fields restricted to the case of characteristic 0. Based on the general principle, some methods of solving such arbitrary polynomial systems may be found. This part also goes back to classical Chinese mathematics as well as treating modern works in this field. Finally, Part III contains applications and examples.

8. Citation
   symposium on Symbolic and algebraic computation toc 1986 , Waterloo, Ontario, Canadageometry theorem proving using Hilbert's Nullstellensatz Author Deepak  
   http://portal.acm.org/citation.cfm?id=32439.32479&coll=portal&dl=ACM&type=series

9. A Combination Of Nonstandard Analysis And Geometry Theorem Proving, With Applica
   The theorem prover Isabelle is used to formalise and reproduce some of the styles of reasoning used by Newton in his Principia. The Principia s reasoning is resolutely geometric in nature but contains infinitesimal elements and the presence of  
   http://citeseer.nj.nec.com/fleuriot98combination.html
   
   Extractions: Abstract: . The theorem prover Isabelle is used to formalise and reproduce some of the styles of reasoning used by Newton in his Principia. The Principia's reasoning is resolutely geometric in nature but contains "infinitesimal" elements and the presence of motion that take it beyond the traditional boundaries of Euclidean Geometry. These present di#- culties that prevent Newton's proofs from being mechanised using only the existing geometry theorem proving (GTP) techniques. Using concepts from... (Update)

10. Citation
    Citation. Mathematics And Its Applications archive Mechanical geometry theoremproving Author SC Chou Publisher Kluwer Academic Publishers Norwell, MA, USA  
    http://portal.acm.org/citation.cfm?id=39060&dl=ACM&coll=portal&CFID=11111111&CFT

11. Citations: Plane Geometry Theorem Proving Using Forward Chaining - Science (Rese
    Plane geometry theorem proving using forward chaining. Artificial Intelligence,6. Nevins, A. (1975). Plane geometry theorem proving using forward chaining.  
    http://citeseer.nj.nec.com/context/289587/0

12. Math Forum: Teacher2Teacher - Post A Reply To "Some Geometry Theorem Tricks"
    Post a reply to the public discussion message Some geometry theoremtricks by Steve Madaris. T2T FAQ Ask T2T Teachers' Lounge  
    http://mathforum.org/t2t/discuss/post_reply.taco?thread=690&n=57

13. Dynamic Geometry Theorem Prover By Jacques Gressier
    Dynamic geometry theorem prover by Jacques Gressier. reply to this messagepost a message on a new topic Back to geometryannouncements  
    http://mathforum.org/epigone/geometry-announcements/permpayzhing
    
    Extractions: Subject: Dynamic geometry theorem prover Author: jacques.gressier@hol.fr Organization: Epigone Date: 21 Jun 1997 11:45:58 -0400 You will find a theorem prover which is the core of a french dynamic geometry software (Windows demo version) at http://wwwperso.hol.fr/~jgressie/index.htm . Much more powerful than SketchPad or Cabri, it can solve any Euclidian geometry problem construction AND proof. ( 75% of the software has been written in Prolog). The teacher can define any new geometry construction exercise. There's also a compiler that can read natural language description of a geometry problem and then generate all possible solutions. The student can try and find the proof. He will be corrected in real time (while defining the figure AND building the proof) and helped to the solution whatever he does. The compiler is not available in the demo version but you can generate construction exercises. We are looking for people who could help us and translate the whole software into other languages. To read articles about experiments in classrooms with this software you can directly go to : http://www.ac-strasbourg.fr/Partenariat/Cari-info/Articles/Anciens/HYPO2COL.htm

14. Jacques D. Fleuriot: CV
    Theorem Proving in Geometry and Nonstandard Analysis My research involves the mechanizationof Nonstandard Analysis and geometry theorem Proving within the  
    http://www.cl.cam.ac.uk/users/jdf21/cv.html
    
    Extractions: United Kingdom I have a background in Artificial Intelligence and theoretical Computer Science. I did my first degree at Imperial College where I was the only student to take the, then newly introduced, Artificial Intelligence and Knowledge Engineering specialist degree. I am currently writing up my PhD thesis. My research is in the field of Interactive Mechanical Theorem Proving. I am a member of the Automated Reasoning Group of the Computer Laboratory. Mechanical Theorem Proving in Geometry and Nonstandard Analysis My research involves the mechanization of Nonstandard Analysis and Geometry Theorem Proving within the formal framework of the generic proof assistant Isabelle. I have developed and applied techniques from both fields to the formalization and mechanization of Newton's Principia. I have also used nonstandard techniques to carry out formalized analysis in Isabelle. This work shows that the clear and synthetic nature of NSA leads to more intuitive and often shorter proofs. This is especially noticeable for epsilon-delta proofs in analysis.

15. Designing And Implementing A Geometry Theorem Prover In Java.
    Designing and Implementing a geometry theorem Prover in Java. Proposer JacquesFleuriot, Phone 0131 650 9342, jdf@dai.ed.ac.uk. SelfProposed No.  
    http://www.dcs.ed.ac.uk/teaching/cs4/projects/proposals/02/props/59_fleuriot1.ht
    
    Extractions: Designing and Implementing a Geometry Theorem Prover in Java. Proposer: Jacques Fleuriot, Phone: 0131 650 9342, jdf@dai.ed.ac.uk Self-Proposed: No Supervisor: Jacques Fleuriot, Phone: 0131 650 9342, jdf@dai.ed.ac.uk Subject Areas: Automated Reasoning/Theorem Proving, Suitable for the following degrees: AI-CS, AI-SE4, AI-Math4, AI-Psych4, CS4, Principal goal of the project: The aim of this project is to develop a mechanical theorem prover in Java that exploits some of the powerful achievements in automated geometry theorem proving. Description of the project: Automated geometry theorem proving (GTP) is one of the most successful areas of automated reasoning. Powerful algebraic techniques such as Wu's [1] and the Groebner Bases [2] methods have been devised in the late 70s and 80s, that are able to prove non-trivial theorems in Euclidean and non-Euclidean geometry automatically. Most of these techniques proceed by introducing a coordinate system and then transforming the geometry problem into an algebraic form that can then be dealt with algorithmically. In the mid 90s, a number of powerful methods have also appeared that aim to combine simple algebraic manipulations with more traditional, heuristic geometric theorem proving techniques. These techniques are based on geometrically intuitive notions such as signed areas [3] and full-angles [4], for example, and are part of the so-called coordinate-free or synthetic approach to GTP.

16. Foundations Of Geometry: Theorem 2
    Theorem 2. If BX. In other words, we're going to hypothesize thatTheorem 2 is false and show that leads to a contradiction. II.  
    http://www.doublebit.com/archives/math/sstp1979/foundations/theorem2.htm
    
    Extractions: If A, B, and C are three non-collinear points and X is a point of AC, then X is the only point on both AC and BX. I. Given non-collinear points A, B, and C, with a point, X, on AC, assume that there is also a point, Y, on both AC and BX. [In other words, we're going to hypothesize that Theorem 2 is false and show that leads to a contradiction]. II. By Axiom III , points X and Y are contained in only one line, contradicting the hypothesis that the points X and Y are contained in both AC and BX. III. Since the hypothesis is false, Theorem 2 must be true.

17. Foundations Of Geometry: Theorem 1
    Theorem 1. If A and C are two points, there is a point P such thatA, C, and P are noncollinear. Jeff's 1979 Notes. I. Given points  
    http://www.doublebit.com/archives/math/sstp1979/foundations/theorem1.htm
    
    Extractions: If A and C are two points, there is a point P such that A, C, and P are non-collinear. I. Given points A and C, there exists a third point, P [ Axiom II II. Since there is only one line which contains both A and C [ Axiom III ], and since the third point, P, cannot also be contained in this line (otherwise contradicting Axiom II), no line contains A, C, and P. III. By Definition 3 , points A, C, and P are non-collinear. Apparently, Axiom II can be broadly interpreted to "manufacture" a non-collinear point with respect to any given line, which would seem to make this a pretty trivial theorem.

18. A Combination Of Geometry Theorem Proving And Nonstandard Analysis With Applicat
    A Combination of geometry theorem Proving and Nonstandard AnalysisWith Application to Buy A Combination of geometry theorem  
    http://www.computerhelpbooks.com/c/Computer_Expert_Systems/A_Combination_of_Geom

19. A Combination Of Geometry Theorem Proving And Nonstandard Analysis With Applicat
    A Combination of geometry theorem Proving and Nonstandard AnalysisWith Application to by Jacques Fleuriot Buy A Combination  
    http://www.computerhelpbooks.com/c/Computer_Expert_Systems/A_Combination_of_Geom
    
    Extractions: A Combination of Geometry Theorem Proving and Nonstandard Analysis With Application to... If you are searching for any of the following topics: Look no further. You'll find A Combination of Geometry Theorem Proving and Nonstandard Analysis With Application to... by Jacques Fleuriot at ComputerHelpBooks.com! At ComputerHelpBooks.com , you'll discover an easy to use site offering books such as A Combination of Geometry Theorem Proving and Nonstandard Analysis With Application to... by Jacques Fleuriot Click here to learn more about A Combination of Geometry Theorem Proving and Nonstandard Analysis With Application to... by Jacques Fleuriot.

20. A Reification Of A Strategy For Geometry Theorem Proving
    A Reification of a Strategy for geometry theorem Proving. Noboru Matsudaand Kurt VanLehn Abstract For many years, designers of ITS  
    http://www.pitt.edu/~mazda/AdvGeo/Doc/ITS2000/
    
    Extractions: Noboru Matsuda and Kurt VanLehn Abstract For many years, designers of ITS have tried to use the power of a well-designed graphical user interface (GUI) to help students learn complex problem solving strategies. The basic idea is to display the reasoning in a graphical, manipulable form - to ``reify'' (make real) the reasoning. In this paper, we point out flaws in some common techniques for reification and suggest a new one. Our basic idea is to reify the search process rather than the structure of the ultimate solution. We show how this reification technique can be applied to a specific complex problem solving task domain, geometry theorem proving with construction, for which we are building an ITS. On-line article to the piblication list Last modified: Feb. 20, 2001

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