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

Next: 5. The Current State Up: 4. Two Examples Previous: 1. INTPS - a 2. GEO - a collection of mechanized geometry theorem proofs 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

a topic from geometry-college Projective Geometry Theorem post a message on this topic post a message on a new topic 5 Sep 1999 Projective Geometry Theorem , by Antreas P. Hatzipolakis 5 Sep 1999 Re: Projective Geometry Theorem , by Dick Tahta 5 Sep 1999 Re: Projective Geometry Theorem , by Antreas P. Hatzipolakis The Math Forum

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/

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

a topic from geometry-college new(?) geometry theorem post a message on this topic post a message on a new topic 3 Sep 1999 new(?) geometry theorem , by F. Alexander Norman 3 Sep 1999 Re: new(?) geometry theorem , by Antreas P. Hatzipolakis 5 Sep 1999 Re: new(?) geometry theorem , by Antreas P. Hatzipolakis The Math Forum

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

Next: 4.iii Further Extensions of the Schubert Calculus Up: 4.ii The Special Schubert Calculus Previous: 4.ii.b. The Degrees of Grassmann Varieties 4.ii.c. Proof of Theorem Consider the action of the non-zero real numbers R x on R n t e j t j e j where t is in R x (a non-zero real number) and e e e n is a basis for R n (corresponding to the rows of the n by n identity matrix). Let L be a ( n k )-plane. By ( ), the equation for a k -plane K to meet t L non-trivially is t n n b L b p b K the sum over all b in C n k . For K in X a the sum is over those b below a (including a ), by ( ). Removing the common factor t n n a gives t a b L b p b K The case l i equal to 1 of Theorem is implied by the case a n k n n of the following theorem, as X = Gr( k n Theorem 4.6 , Theorem 4.2]) Let L be a real real ( n k t t t k n k in R x such that for every a in C n k the intersection of the Schubert varieties X a X t L X t L X t a L is transverse (so it contains d a ) points) with all points real. Proof. We induct on m to construct numbers t t t k n k in R x having the property that, for all a in C n k a m , the intersection of the Schubert varieties X a X t L X t L X t m L is transverse (over C ) and each of its d a ) points are real.

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

Title Authors Affiliation ISBN ISSN advanced search search tips Books Mechanical Geometry Theorem Proving Mechanical Geometry Theorem Proving Kluwer Academic Publishers is pleased to make this title available as a special Printing on Demand (PoD) edition. PoD books will be sent to you within 6-9 weeks of receipt of your order. Firm orders only!: returns cannot be accepted as PoD books are only printed on request. Add to cart by Shang-Ching Chou Materials Technology Laboratory, U.S. Army, Watertown, MA, USA Book Series: MATHEMATICS AND ITS APPLICATIONS Volume 41 Review(s) This work is, in my opinion, completely revolutionary. I believe that, by itself, the book will convince any mathematician in the world that the automation of mathematical reasoning is a profound and rewarding enterprise of extraordinary potential. Robert S. Boyer D. Reidel Publishing Company Hardbound, ISBN 90-277-2650-7 December 1987, 372 pp. Printing on Demand EUR 214.00 / USD 270.00 / GBP 162.75 Paperback, ISBN 1-4020-0330-7 November 2001, 372 pp. Printing on Demand EUR 75.00 / USD 68.00 / GBP 47.25

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

Title Authors Affiliation ISBN ISSN advanced search search tips Books Mathematics Mechanization Mathematics Mechanization Mechanical Geometry Theorem-Proving, Mechanical Geometry Problem-Solving and Polynomial Equations-Solving Add to cart by Wu Wen-tsun Mathematics Mechanization Research Center, Institute of Systems Science, Chinese Academy of Sciences, Beijing, PRC Book Series: MATHEMATICS AND ITS APPLICATIONS Volume 489 This book is a collection of essays centred around the subject of mathematical mechanization. It tries to deal with mathematics in a constructive and algorithmic manner so that reasoning becomes mechanical, automated and less laborious. 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. Audience: This volume will be of interest to research and applied mathematicians, computer scientists and historians in mathematics.

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

A Combination of Nonstandard Analysis and Geometry Theorem Proving, with Application to Newton's Principia (1998) (Make Corrections) (5 citations) Jacques D. Fleuriot, Lawrence C. Paulson Lecture Notes in Computer Science Home/Search Context Related View or download: cl.cam.ac.uk/users principCADE.ps.gz cl.cam.ac.uk/users principCADE.ps.gz ... 14210003.pdf Cached: PS.gz PS PDF DjVu ... Help From: cl.cam.ac.uk/users/lcp refereed (more) From: springerny.com/link/serv Homepages: J.Fleuriot L.Paulson HPSearch (Update Links) Rate this article: (best) Comment on this article (Enter summary) 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) Context of citations to this paper: More ...cl.cam.ac.uk Abstract. The approach previously used to mechanise lemmas and Kepler s Law of Equal Areas from Newton s Principia is here used to mechanically reproduce the famous Propositio Kepleriana or Kepler Problem.

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

Cognitive Science, 11. Nevins, A. (1975). Plane geometry theorem proving using forward chaining . Artificial Intelligence, 6. Home/Search Document Not in Database Summary Related Articles This paper is cited in the following contexts: Spatial Aggregation: Theory and Applications - Yip (1996) (9 citations) (Correct) No context found. Cognitive Science, 11. Nevins, A. (1975). Plane geometry theorem proving using forward chaining . Artificial Intelligence, 6. Online articles have much greater impact More about CiteSeer Add search form to your site Submit documents CiteSeer - citeseer.org Terms of Service NEC Research Institute

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

Dynamic geometry theorem prover by Jacques Gressier reply to this message post a message on a new topic Back to geometry-announcements 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

J. D. Fleuriot : Curriculum Vitae Name: Jacques D. Fleuriot Date of Birth: Nationality: Mauritian Email: Jacques.Fleuriot@cl.cam.ac.uk Address: Computer Laboratory University of Cambridge New Museums Site Pembroke Street Cambridge CB2 3BQ United Kingdom Telephone Precis Automated reasoning - Mechanical Theorem Proving Logic and Mathematics Artificial intelligence and Knowledge Engineering Theoretical Computer Science 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. Education Research Student Computer Laboratory, University of Cambridge 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

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

Theorem 2 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. Jeff's 1979 Notes 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

Theorem 1 If A and C are two points, there is a point P such that A, C, and P are non-collinear. Jeff's 1979 Notes 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. Jeff's 2000 Notes 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

All Products Books Pop Music Classical Music Videos Consumer Electronics Software Kitchen Search by keywords: Search: Auctions The Web Books Music Electronics Forums Hardware Jobs Software Toys Video Games Links Our Online Mall Our Other Sites How To Use This Site ... Privacy Statement Related Sites Digital Cameras Computer Printers Digital Cameras Digital Cameras ... Adapt, Inc. Computer Expert Systems Bookstore A Combination of Geometry Theorem Proving and Nonstandard Analysis With Application to... by Jacques Fleuriot Sales Rank - 1,189,790 Jacques Fleuriot MORE INFO by ALPHABETICAL 1 of 100 ITEMS Previous Next by CUSTOMER REVIEW 47 of 100 ITEMS Previous Next by SALES RANK 47 of 100 ITEMS Previous Next More Computer Expert Systems Items Related

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

A Combination of Geometry Theorem Proving and Nonstandard Analysis With Application to... If you are searching for any of the following topics: A Combination of Geometry Theorem Proving and Nonstandard Analysis With Application to... A Combination of Geometry Theorem Proving and Nonstandard Analysis With Application to... by Jacques Fleuriot A Combination of Geometry Theorem Proving and Nonstandard Analysis With Application to... by Jacques Fleuriot reviews BUY A Combination of Geometry Theorem Proving and Nonstandard Analysis With Application to... ... PURCHASE A Combination of Geometry Theorem Proving and Nonstandard Analysis With Application to... 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/

A Reification of a Strategy for Geometry Theorem Proving 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 PDF format (102KB) to the piblication list Last modified: Feb. 20, 2001 Noboru Matsuda

Page 1     1-20 of 92    1  | 2  | 3  | 4  | 5  | Next 20