41. Stottler Henke - Artificial Intelligence History Herbert Gelernter wrote the geometry theorem Prover which used information to prune a search with a billion alternatives (for a 3step proof of a geometry http://www.stottlerhenke.com/ai_general/history.htm

Home Our Company Products Solutions ... Using AI History A papyrus, that was bought in a Luxor antique shop by Edwin Smith in 1882, was prepared representing 48 surgical observations of head wounds. The observations were stated in symptom-diagnosis-treatment-prognosis combinations as: IF a patient has this symptom, THEN he has this injury with this prognosis if this treatment is applied. This was the first known expert system. th C Leviathan, written by Thomas Hobbes (1588­1679), was published. In it he proposes that humans collectively, by virtue of their organization and use of their machines, would create a new intelligence. George B. Dyson refers to Hobbes as the patriarch of artificial intelligence in his book, "Darwin Among the Machines: The Evolution of Global Intelligence," p7, 1997. th C Leibnitz and Pascal invented mechanical computing devices. Pascal was 19 years old in 1642 when he invented an eight-digit calculator, the Pascaline. In 1694, Gottfried Liebnitz invented the Liebnitz Computer, which multiplied by repetitive addition, an algorithm still in use today. Leibnitz also conceived of a 'reasoning calculator' for interpreting and evaluating concepts, but realized the problem was immense because of the great interconnectedness of concepts. Jonathan Swift anticipated an automatic book writer in Gulliver's Travels.

42. History Of Geometry He proved many projective geometry theorems, the earliest including Pascal s mystic hexagon (1639). Leonhard Euler (17071783) http://geometryalgorithms.com/history.htm

History Home Overview [History] Algorithms Books Web Sites Gift Shop 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 the following links for recommended: Books about Geometry History Web Sites about Geometry History Greek Medieval ... Ancient Geometry (30000 BC - 500 BC) Babylon (4000 BC - 500 BC) Egypt (5000 BC - 500 BC) 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 . One of the few surviving documents was written by: Ahmes 1680-1620 BC) wrote the Rhind Papyrus (aka the Ahmes Papyrus). In it, he claims to not be the author, but merely a scribe of material from an earlier work of about 2000 BC. It contains rules for division, and has 87 problems including the solution of equations, progressions, volumes of granaries, etc.

43. AAutomated Deduction In Geometry The SymbolicData GEO Records A Public Repository of geometry theorem Proof Emphasizing Human Techniques in Automated geometry theorem Proving A http://wotan.liu.edu/docis/dbl/adgadg/

The Digital Librarian's Digital Library search D O Do C omputing and I S cience Home Journals and Conference Proceedings aAutomated Deduction in Geometry Algorithmic Tests for the Normal Crossing Property Using Computer Algebra Tools to Classify Serial Manipulators Solen Corvez, Fabrice Rouillier Irina Tchoupaeva C1 Spline Implicitization of Planar Curves Distance Coordinates Used in Geometric Constraint Solving Lu Yang Algebraic Representation, Elimination and Expansion in Automated Geometric Theorem Proving Hongbo Li The SymbolicData GEO Records - A Public Repository of Geometry Theorem Proof Schemes Function-Based Shape Modeling: Mathematical Framework and Specialized Language Alexander A. Pasko, Valery Adzhiev MMP/Geometer - A Software Package for Automated Geometric Reasoning Xiao-Shan Gao, Qiang Lin A New Structural Rigidity for Geometric Constraint Systems Christophe Jermann, Bertrand Neveu, Gilles Trombettoni The Nonsolvability by Radicals of Generic 3-connected Planar Graphs John C. Owen, Steve C. Power GEOTHER 1.1: Handling and Proving Geometric Theorems Automatically Dongming Wang The Projection of Quasi Variety and Its Application on Geometric Theorem Proving and Formula Deduction XueFeng Chen, DingKang Wang

44. Mathematics: Pre98 Bulmer, M, Stokes, TE, ‘geometry theorem Prover’, Mathematica World, 3 (10) 116 (1995) A2. Bulmer, M, ‘The Cost of Subsistence’, Mathematica World, http://www.research.utas.edu.au/reports/1995/d1995d25.htm

UTAS Home Contacts Search UTAS Research Home Grants and Funding Human Ethics Animal Ethics ... Contacts 1995 Research Report Journal Article Numerische Mathematik Journal of Computational and Applied Mathematics Algebra Universalis Journal of Pure and Applied Algebra Semigroup Forum Journal of the Australian Mathematical Society, Ser. A Bulletin of the London Mathematical Society. Communications in Algebra Glasgow Mathematical Journal Journal of Algebra Russian Mathematics (Izvestiya Vysshikh Uchebnykh Zavedenii Matematika) Acta Mathematicae Universitatis Comenianae Journal of Algebra Bulletin of the Australian Mathematical Society Publicationes Mathematicae (Debrecen) Mathematica World Archiv der Mathematik Journal of Physics A. Journal of Pure and Applied Algebra Mathematica World Mathematica World Mathematica World Mathematica World Mathematica World Mathematica World Mathematica World The Australian Computer Journal International Astronomical Union Circular Conference Publication 15th Biennial Conference of the Australian Association of Mathematics Teachers , Darwin, 65-71 (1995) CANT'95 , Sydney, 121-127 (1995) Thesis p EJ - Denotes Electronic Journal *Not a member of this University.

45. Automated Development Of Fundamental Mathematical Theories By Art Quaife Moreover, essential features of the geometry theorem proving algorithm do carry Gelerntner, H. (1963) Realization of a geometry theoremproving machine. http://psyche.cs.monash.edu.au/v2/psyche-2-28-fearnley_sande.html

This book may be purchased from Amazon.Com Automated Theorem Proving and Its Prospects Review of Automated Development of Fundamental Mathematical Theories by Art Quaife Desmond Fearnley-Sander Department of Mathematics University of Tasmania HOBART TAS 7001 AUSTRALIA dfs@hilbert.maths.utas.edu.au Received: December 28, 1995; Accepted: March 17, 1996; Published: June 19, 1996 PSYCHE, 2(28), June 1996 http://psyche.cs.monash.edu.au/v2/psyche-2-28-fearnley_sande.html KEYWORDS: automated theorem proving, OTTER, Quaife, resolution, understanding. REVIEW OF: Automated Development of Fundamental Mathematical Theories by Art Quaife (1992). Kluwer Academic Publishers. 271pp. $US123 hbk. ISBN: 0-7923-2021-2. 1. Introduction In his recent books one of the main pre-occupations of Roger Penrose has been to show (to prove!) that computers are intrinsically limited, compared to humans, when it comes to the doing of mathematics. Even those who think that such things can be proved may be interested in the empirical question: what mathematics can computers do? Art Quaife's book addresses the aspect of doing mathematics that is reported in mathematical journals: proof of theorems. It shows us the extent to which this high exercise of rationality can currently be automated, and the extent to which it cannot. To me this book was fascinating. After reading it, I found myself turning over in my mind the question of the role played in theorem proving by understanding, a quality that Penrose regards as a prime desideratum of consciousness. I'll come back to that at the end of this review.

46. Abstract: Geometry Theorem Proving Package In SCRATCHPAD II: A Primer geometry theorem Proving Package in SCRATCHPAD II A Primer. Herwig Mayr RISC–Linz Series no. 88–1.0, RISC–Linz, Dept. of Mathematics, Univ. http://webbler.fhs-hagenberg.ac.at/webbler.exe?database=standort.mdb&getpagename

47. Abstract: A Geometry Theorem Proving Package In SCRATCHPAD II Translate this page A geometry theorem Proving Package in SCRATCHPAD II. Johann Heinzelreiter, Herwig Mayr, K. Kusche, B. Kutzler Proc. http://webbler.fhs-hagenberg.ac.at/webbler.exe?database=standort.mdb&getpagename

48. Symbolic Computation We developed a refutational approach for geometry theorem proving both using \Groebner basis algorithm as well as characteristic set method. http://www.cs.albany.edu/ipl/symb.comp.html

Symbolic Computation List of Related Publications Elimination Methods: An Introduction Symbolic and Numerical Computation for Artificial Intelligence , Donald, Kapur and Mundy (eds.), Academic Press, 1992, 45-87. Deepak Kapur and Lakshman Y.N. Automated Deduction in Geometry Deepak Kapur Automated Deduction in Geometry Deepak Kapur Extraneous Factors in the Dixon resultant formulation International Symposium on Symbolic and Algebraic Computation (ISSAC-97) , August 1997, Maui, Hawaii Deepak Kapur and T. Saxena Sparsity Considerations in Dixon Resultants Proc. of 28th Annual ACM Symposium on Theory of Computing, (STOC '96), Philadelphia, PA, May, 1996. Deepak Kapur and Tushar Saxena A Refutational Approach to Geometry Theorem Proving Journal of Artificial Intelligence , Vol. 37, Dec. 1988, 61-93. Deepak Kapur Extraneous Factors in the Dixon Resultant Formulation Proc. of International Symposium on Symbolic and Algebraic Computation (ISAAC-97) , Maui, Hawaii, August 1997. Deepak Kapur and Tushar Saxena Comparison of Various Multivariate Resultant Formulations Proc. of

49. Alessandra Mariotti Et Al. 1997 Approaching geometry theorems in contexts from history and epistemology to To approach geometry theorems in this sense, the features of the field of http://www.lettredelapreuve.it/Resumes/Mariotti/Mariotti97.html

50. P. Boero, G. Chiappini, R. Garutti Et A. Sibilla 1992 Proving geometry theorems prevails also in high school students work (see Moore, 1994). Similarly to the approach to geometry theorems, historical and http://www.lettredelapreuve.it/Resumes/Boero/Boero95.html

51. JCST-Vol.19, No.6, September 2004 Abstract WeiWen Xu (812) geometry theorem Proving by Decomposing Polynomial Systems into Strong Two examples are given to show that the geometry theorems are http://jcst.ict.ac.cn/conc/conc46.html

52. GeoProver Version 1.3a The GeoProver Package for Mechanized (Plane) geometry theorem Proving It contains many (generic) proof schemes of geometry theorems, mainly from Chou s http://www.informatik.uni-leipzig.de/~graebe/ComputerAlgebra/Software/GeoProver/

The GeoProver Package for Mechanized (Plane) Geometry Theorem Proving Version 1.3a Freezed at Jan 18, 2003 AUTHOR Hans-Gert Graebe ADDRESS Univ. Leipzig, Institut f. Informatik, D - 04109 Leipzig, Germany URL http://www.informatik.uni-leipzig.de/~graebe EMAIL graebe@informatik.uni-leipzig.de Key Words geometry theorem proving Introduction The GeoProver is a small package for mechanized (plane) geometry manipulations with non degeneracy tracing, available for different CAS platforms (Maple, MuPAD, Mathematica, and Reduce). It provides the casual user with a couple of procedures that allow him/her to mechanize his/her own geometry proofs. Version 1.1 grew out from a course of lectures for students of computer science on this topic held by the author at the Univ. of Leipzig in fall 1996 and was updated after a similar lecture in spring 1998. The (completely revised) version 1.2, finished in March 2002, was set up as a generic software project to manage the code for different platforms in a unified way. There is a close relationship to the SymbolicData project (see http://www.symbolicdata.org

53. VL Geometrie Mit Dem Computer geometry theorem Proving on the Computer. Participants. Students of computer science and S.C. Chou Mechanical geometry theorem proving. Kluwer Acad. http://www.informatik.uni-leipzig.de/~graebe/vorlesungen/englisch/geometrie.html

Geometry Theorem Proving on the Computer Participants: Students of computer science and mathematics that will learn more about applications of symbolic computations. Credits as special course of applied or theoretical computer science. Overview: In the course the audience will learn more about different symbolic methods, that proved useful in applications to geometric problem solving. Structure: Introduction to geometric problems Symbolic representation of geometric constructions Geometry theorems of constructive type Geometry theorems of equational type Different higher algebra approaches Examples Literature: S.-C. Chou: Mechanical geometry theorem proving. Kluwer Acad. Publishers, Dordrecht 2002. S.-C. Chou u.a.: Machine Proofs in Geometry - Automated Production of Readable Proofs for Geometry Theorems. World Scientific, Singapore 1994 . D. Cox, J. Little, D. O'Shea : Ideals, varieties, and algorithms. Springer, New York 1992. H.S.M. Coxeter and S.L. Greitzer : Geometry revisted. Toronto - New York, 1967. W. Wu: Mechanical theorem proving in geometries. Springer, Wien 1994.

54. Chapter 2 - Some Scenarios We may now use the new class in demonstrating a geometry theorem. The theorem states that given an arbitrary quadrilateral, if one bisects each of the sides http://www.2share.com/thinglab/ThingLab - Chapter 2.html

Chapter 2 - Some Scenarios An Introductory Example This chapter presents some examples of ThingLab in operation. As an introductory example, we will use ThingLab to construct a quadrilateral and view it in several ways. We will then use the system to demonstrate a theorem about quadrilaterals. Before presenting the example, a brief introduction to the ThingLab user interface is needed. The user interacts with ThingLab via a window , a rectangular area on the computer’s display. The window notion is central to Smalltalk’s user interface philosophy. The ThingLab window described here is typically one of several windows on the screen, with other windows being available for debugging, editing system code, freehand sketching, and so on. [ Figure 2.1 - A Smalltalk display The ThingLab window is divided into five panes: the class pane, the format pane, the messages pane, the arguments pane, and the picture pane. The class pane is a menu of names of classes that may be viewed and edited. Once a class has been selected, a menu of formats in which it can display itself appears in the pane immediately to the right. The class shows itself in the chosen format in the large pane at the bottom of the window labeled picture.

55. ICAI '99 -- Automatted Geometry Theorem Proving Automatted geometry theorem Proving. Judit Robu. Abstract. Mechanical geometry theorem proving is a classic artificial intelligence subject. http://sztech.ektf.hu/icai01/abstracts/robujudit.html

Automatted Geometry Theorem Proving Judit Robu Abstract Mechanical geometry theorem proving is a classic artificial intelligence subject. Several methods were developed, with very different mathematical background, some of them being quite efficient in proving constructive geometry theorems. I present some of these methods, as the characteristic set method and the area method.

56. ENC Online: Curriculum Resources: Browse: Mathematics> Geometry> Theorems Browse Mathematics Geometry Theorems a mix of Incan history with illustrated, animated stepby-step proofs of not commonly found geometry theorems. http://www.enc.org/resources/browse/0,,0-100-294-1165_1_0-0-0,00.shtm

Skip Navigation You Are Here ENC Home Curriculum Resources Browse Search the Site More Options Don't lose access to ENC's web site! Beginning in August, goENC.com will showcase the best of ENC Online combined with useful new tools to save you time. Take action todaypurchase a school subscription through goENC.com Classroom Calendar Digital Dozen ENC Focus ... Ask ENC Explore online lesson plans, student activities, and teacher learning tools. Search Browse Frequently Asked Questions Resource of the Day ... About Curriculum Resources Read articles about inquiry, equity, and other key topics for educators and parents. Create your learning plan, read the standards, and find tips for getting grants. 14 Records Sorted by Date Use these menus to limit browse results using specific criteria Grade: All Grade Levels Pre-K to 2 3 to 5 6 to 8 9 to 12 Post Sec. Media Type: All Media Types Only Web Sites Excluding Web Sites Cost: All Costs Low Cost (Less than $50) Free Return to Subject Tree Modify using Advanced Search Geometry Java applet gallery ENC Digital Dozen Site Date: Grade(s): 9 - Post Sec.

57. Predrag Janicic Predrag Janicic, Stevan Kordic EUCLID the geometry theorem Prover, FILOMAT, Nis, EUCLID ((c) 1992,1996; geometry theorems Prover; runs under MS DOS) http://www.matf.bg.ac.yu/~janicic/

Predrag Janicic Personal Page Predrag JANICIC assistant professor Faculty of Mathematics Studentski trg 16 11000 Belgrade e-mail: janicic@matf.bg.ac.yu url: www.matf.bg.ac.yu/~janicic General Information Education and Degrees Collaborations and Cooperations ... Teaching General Information Contact Information Faculty of Mathematics Studentski trg 16 11000 Belgrade e-mail: janicic@matf.bg.ac.yu url: www.matf.bg.ac.yu/~janicic Information for Visitors The office in Simina 2 and the office 839 in the Faculty of Mathematics Professional History I was born in December of 1968 in the city of Pristina , Serbia, Yugoslavia where I graduated from “Miladin Popovic” High School in 1987. After a year of obligatory Army service, in October of 1988 I enrolled the University of Belgrade, Faculty of Mathematics , Department of Computer Science. I graduated from University in 1993. My GPA (grade point average) was highest possible (10.00). The same year I was offered position of a Teaching Assistant. During 1996, 2001, and 2002 I worked eight months as a visiting researcher at prof. Alan Bundy's Mathematical Reasoning Group (School of Informatics, University of Edinburgh). In 1996 I received my MSc degree and in 2001 my PhD degree in Computer Science from the Faculty of Mathematics, University of Belgrade. Since October 2001, I work as an assistant professor and presently teach a course in Mathematical Logic in Computer Science and a course in Computer Graphics. My research interests are in the field of Automated Reasoning. I am a member of

58. ATIP95.91 : Mathematical Mechanization In China An efficient decomposition algorithm for geometry theorem proving, Recent advance of automated geometry theorem proving with high level geometry http://www.atip.org/public/atip.reports.95/atip95.91r.html

ATIP95.91 : Mathematical Mechanization in China ASIAN TECHNOLOGY INFORMATION PROGRAM (ATIP) REPORT: ATIP95.91 : Mathematical Mechanization in China To: Distribution From: D.K.Kahaner, [ kahaner@atip.or.jp ] This is file name "atip95.91" Date: 24 Nov 1995 ATIP95.91 : Mathematical Mechanization in China ABSTRACT: This report is twofold: First, we give a brief introduction to the Mathematical Mechanization Research Center (MMRC) in China. This Center is among the most influential in China studying the interplays between mathematics and computer science (including computer algebra, computer vision, CAD, machine reasoning, machine proof of geometric theorems, and robotics). Second, we present an overview of a conference held at the MMRC, The First Asian Symposium on Computer Mathematics (ASCM'95), which was mainly attended by Asian researchers in mathematical mechnization including mechanical engineering. START OF REPORT ATIP95.91 The remaining sections of this report are available to ATIP subscribers ] Tokyo Office: Asian Technology Information Program (ATIP) Harks Roppongi Building 1F 6-15-21 Roppongi, Minato-ku, Tokyo 106 Tel: +81 3 5411-6670; Fax: +81 3 5411-6671 U.S. Office: Asian Technology Information Program (ATIP) P.O. Box 9678, Albuquerque, New Mexico 87119-9678 Tel: (505)-842-9020; Fax: (505)-766-5166 For further information Send email to :

59. Generation5 - The History Of AI problems led to the initiation of projects such as Logic Theorist (considered as the first AI program), geometry theorem Prover, and SAINT. http://www.generation5.org/content/1999/aihistory.asp

Home Articles Reviews Interviews ... Contribute Login Login: Password: Keep me logged in. ( help Register Why register? Lost your password? ... MobES Expert System Friends and Affiliates Home Articles General > Miscellaneous The History of AI By Edward Kao Printable Version Mankind has long been curious about how the mind works and fascinated by intelligent machines. From Talos, the copper giant in Iliad , Pinocchio, the fairy wooden puppet acting like a real boy, and the early debates on the nature of the mind and thought by European philosophers and mathematicians, we can see people's desire to understand and even to create intelligence. The Birth of AI (1945-56) However, it wasn't until the postwar period (1945-1956) that Artificial Intelligence would emerge as a widely-discussed field. What propelled the birth of Artificial Intelligence were the arrival of modern computer technology and the arise of a critical mass. Pioneers such as Marvin Minsky , John McCarthy, Allen Newell, and Herbert Simon led their students in defining the new and promising field. The development of the modern computer technology effected the AI research tremendously. Many pioneers of AI broke away from the traditional approach of artificial neurons and decided that the human thought could be more efficiently emulated with modern digital computer. Those who did not accept digital computers as the new approach stayed in the parallel field of neural network The Dawning Age of AI (1956-63) The Dartmouth Conference of 1956 brought AI to a new era. 1956-1963 represents the dawning of a an intensive AI wave. During this period, major AI research centers such as

60. Campus Event Calendar: Jinzhao Wu (04/07/1999 In 46.1/024) Algebraic Approaches to geometry theorem Proving. Speaker. Jinzhao Wu. From. MaxPlanck-Institut für Informatik. If other. Event Type http://domino.mpi-sb.mpg.de/internet/events.nsf/0/ce78bcfd9b00c7c0c125673c00530d

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