Geometry.Net - Theorems_And_Conjectures: Geometry Theorem

American Mathematical Monthly, The: Geometry: Theorems And Constructions
Full text of the article, geometry theorems and Constructions from American Mathematical Monthly, The, a publication in the field of Reference
http://www.findarticles.com/p/articles/mi_qa3742/is_200205/ai_n9072729

Extractions: Save a personal copy of this article and quickly find it again with Furl.net. It's free! Save it. Geometry, T(14-16: 1). Geometry: Theorems and Constructions. Allan Berele, Jerry Goldman. Prentice Hall, 2001, xii + 232 pp. [ISBN 0-13-087121-41 Claims to be a sophisticated treatment of traditional high school geometry content. Emphasizes proofs in both presentation and exercises; some proofs are tied to constructions. Ignores axioms; begins with a definition of triangle congruence and three triangle congruence theorems. Includes several chapters on advanced triangle theorems (e.g., Ceva's Theorem) and short chapters on solid, spherical, and hyperbolic geometry. MW Reviewers DB: David Bressoud, Macalester; JNC: Judith N. Cederberg, St. Olaf; LC: Laura Chihara, Carleton; JD: Jill Dietz, St. Olaf; PG: Philip Gloor, St. Olaf; BH: Bruce Hanson, St. Olaf; LCL: Loren C. Larson, St. Olaf; RM: Richard Molnar, Macalester; AWR: A. Wayne Roberts, Macalester; MW: Martha Wallace, St. Olaf.
AoPS Math Forum :: View Forum - Geometry Theorems And Formulas
English version geometry theorems and Formulas, Change the language No new posts, Weird geometry theorem billzhao, 4, 1172, Sun Jul 25, 2004 317 pm
http://www.artofproblemsolving.com/Forum/forum-50-50-50.html
AoPS Math Forum :: View Forum - Geometry Theorems And Formulas
English version geometry theorems and Formulas, Change the language View posts since last visit View unanswered posts
http://www.artofproblemsolving.com/Forum/forum-50.html
Computer Laboratory - Technical Report UCAM-CL-TR-442
A combination of nonstandard analysis and geometry theorem proving, with application to Newtons Principia. Jacques Fleuriot, Lawrence C. Paulson
http://www.cl.cam.ac.uk/TechReports/UCAM-CL-TR-442.html

Extractions: Technical Report UCAM-CL-TR-442 Computer Laboratory Research Publications Technical Reports ... Technical Report UCAM-CL-TR-442 JacquesÂ Fleuriot, LawrenceÂ C.Â Paulson January 1998, 13 pages The theorem prover Isabelle is used to formalise and reproduce some of the styles of reasoning used by Newton in his Principia. The Principiaâs reasoning is resolutely geometric in nature but contains âinfinitesimalâ elements and the presence of motion that take it beyond the traditional boundaries of Euclidean Geometry. These present difficulties that prevent Newtonâs proofs from being mechanised using only the existing geometry theorem proving (GTP) techniques. Using concepts from Robinsonâs Nonstandard Analysis (NSA) and a powerful geometric theory, we introduce the concept of an infinitesimal geometry in which quantities can be infinitely small or infinitesimal. We reveal and prove new properties of this geometry that only hold because infinitesimal elements are allowed and use them to prove lemmas and theorems from the Principia. PS Â (0.1Â MB)
2. GEO - A Collection Of Mechanized Geometry Theorem Proofs
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., [
ICME-8// TG19// E-Poster: AutoDiscovery Elementary Theorems//T.Recio//Abstract
Automatic Discovery of Elementary geometry theorems. A technique is presented, based on the computer algebra software CoCoA, for computer oriented
http://mathforum.org/mathed/seville/recio/abstract.html

Extractions: ABSTRACT Automatic Discovery of Elementary Geometry Theorems A different kind of application appears in the next construction: an equilateral triangle and an arbitrary point in the plane are given. We consider the distances of this point to the three lines supporting the sides of the triangle. Our program will then tell us that there is just one possible theorem involving these data, namely, the sum of the distances (affected of certain signs) must be constant.
Math Forum - Ask Dr. Math
From Jeffrey S. Pankewich Subject Euclidian geometry theorem Dr. Math, From Doctor Peterson Subject Re Euclidian geometry theorem Hi, Jeffrey.
http://mathforum.org/library/drmath/view/61453.html

Extractions: Associated Topics Dr. Math Home Search Dr. Math Date: 10/11/2002 at 02:45:00 From: Jeffrey S. Pankewich Subject: Euclidian Geometry theorem Dr. Math, I am studying to be a middle school math teacher, and I am taking a Foundations of Geometry course. We have come to a theorem that our group just can't figure out. The theorem (IX. 16) states, "The bisector of an interior angle of a triangle divides the opposite side internally into two segments which are proportional to the adjacent sides." If you could provide any help, we would greatly appreciate it. Thank you, Jeffrey S. Pankewich Date: 10/11/2002 at 13:02:08 From: Doctor Peterson Subject: Re: Euclidian Geometry theorem Hi, Jeffrey. As often happens, this becomes easy if you draw some extra lines, and get a few little insights. Rather than show you, let me ask a couple questions so you can enjoy the "ahah!" moment yourself. Here's a picture illustrating the theorem: What's interesting about the angle bisector? If you recall that it is used in finding the incenter of the triangle, or have studied loci, you will know that every point on the angle bisector is equidistant from the two legs of the angle. There's only one point in our picture on this bisector, other than vertex C itself. Draw some line segments from that point, related to the fact I just mentioned, and mark what you know about them. Now look at the triangles ACD and BCD. What do you know about their AREAS? If you need more help, please write back and show me how far you got. - Doctor Peterson, The Math Forum
GRAMY
GRAMY A geometry theorem Prover Capable of Construction Some geometry theorems require construction as a part of the proof.
http://www-2.cs.cmu.edu/~mazda/Doc/JAR04/

Extractions: University of Pittsburgh Journal of Automated Reasoning, 32(1), 3-33 (2004) Abstract Keywords : Automated geometry theorem proving, construction, search control, constraint satisfaction problem, intelligent tutoring system (PDF, 281KB) GRAMY project web cite: Advanced Geometry Intelligent Tutoring System affiliated with CIRCLE
GTP - Geometry Theorem Prover
GTP (geometry theorem Prover) GTP is an acronym for * geometry theorem Prover. Web Security Are you really secure? Use our free Web Security
http://www.auditmypc.com/acronym/GTP.asp

Extractions: Every attempt has been made to provide you with the correct acronym for GTP. If we missed the mark, we would greatly appreciate your help by entering the correct or alternate meaning in the box below. Definitions have been compiled from popular search engines and multiple results provided for your review. Iraqi Dinar
Compare Prices And Read Reviews On Mathematics Mechanization: Mechanical Geometr
Mathematics Mechanization Mechanical geometry theoremProving, Mechanical Geometry Problem-Solving, and Polynomial Equations-Solving
http://www.epinions.com/Mathematics_Mechanization_Mechanical_Geometry_Theorem_Pr
Enumerative Real Algebraic Geometry: Theorem 4.4
The case li equal to 1 of Theorem 4.4 is implied by the case a = (nk+1, By Theorem 4.5, Z0 is the union of the Schubert varieties Xb for all b in Cn
http://www.math.tamu.edu/~sottile/pages/ERAG/S4/2.3.html
Elsevier.com - Mathematics Mechanization And Applications
S. Chou, D. Lin, Wu s Method for Automated geometry theorem Proving and Discovering. H. Li, Mechanical Theorem Proving in Differential Geometry.
http://www.elsevier.com/wps/product/cws_home/675328

Extractions: Home Site map Regional Sites Advanced Product Search ... Mathematics Mechanization and Applications Book information Product description Audience Author information and services Ordering information Bibliographic and ordering information Conditions of sale Book related information Submit your book proposal Other books in same subject area About Elsevier Select your view MATHEMATICS MECHANIZATION AND APPLICATIONS Researchers, practitioners and graduate students in symbolic and algebraic computation, geometric reasoning, authomated theorem proving, algorithmic mathematics, and computer-aided mathematical problem solving; researchers and university teachers in computer-aided instruction and education; and software developers, researchers and engineers in mechanics, computer-aided geometric design, geometric modeling, robotics, and computer vision.
ABSJAR
GRAMY A geometry theorem prover capable of construction. Some geometry theorems require construction as a part of the proof.
http://www.pitt.edu/~vanlehn/Stringent/Abstracts/04JAR_NM_KVL.html
DBLP: Shang-Ching Chou
17, ShangChing Chou A geometry theorem Prover for Macintoshes. 1, Shang-Ching Chou, William F. Schelter Proving geometry theorems with Rewrite Rules.
http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/c/Chou:Shang=Ching.htm

Extractions: List of publications from the DBLP Bibliography Server FAQ Coauthor Index - Ask others: ACM DL ACM Guide CiteSeer CSB ... Google Shang-Ching Chou, Xiao-Shan Gao : Automated Reasoning in Geometry. Handbook of Automated Reasoning 2001 Shang-Ching Chou, Xiao-Shan Gao Jing-Zhong Zhang : A Deductive Database Approach to Automated Geometry Theorem Proving and Discovering. J. Autom. Reasoning 25 EE Jian-Xin Ge , Shang-Ching Chou, Xiao-Shan Gao : Geometric constraint satisfaction using optimization methods. Computer-Aided Design 31 EE Xiao-Shan Gao , Shang-Ching Chou: Solving geometric constraint systems. I. A global propagation approach. Computer-Aided Design 30 EE Xiao-Shan Gao , Shang-Ching Chou: Solving geometric constraint systems. II. A symbolic approach and decision of Rc-constructibility. Computer-Aided Design 30 Lu Yang Xiao-Shan Gao , Shang-Ching Chou, Jing-Zhong Zhang : Automated Production of Readable Proofs for Theorems in Non-Euclidian Geometries. Automated Deduction in Geometry 1996 Shang-Ching Chou, Xiao-Shan Gao Jing-Zhong Zhang : An Introduction to Geometry Expert. CADE 1996 Shang-Ching Chou
DBLP: Xiao-Shan Gao
XiaoShan Gao, Jing-Zhong Zhang Automated geometry theorem Proving by Vector Xiao-Shan Gao Ritt-Wu s Decomposition Algorithm and geometry theorem
http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/g/Gao:Xiao=Shan.html

Extractions: List of publications from the DBLP Bibliography Server FAQ Coauthor Index - Ask others: ACM DL ACM Guide CiteSeer CSB ... EE Xiao-Shan Gao, Ming Li : Rational quadratic approximation to real algebraic curves. Computer Aided Geometric Design 2004 EE Xiao-Shan Gao, Ming Li : Rational Quadratic Approximation to Real Plane Algebraic Curves. GMP 2004 EE Ruyong Feng , Xiao-Shan Gao: Rational general solutions of algebraic ordinary differential equations. ISSAC 2004 EE Xiao-Shan Gao, Mingbo Zhang : Decomposition of differential polynomials with constant coefficients. ISSAC 2004 EE Ruyong Feng , Xiao-Shan Gao: Polynomial General Solutions for First Order Autonomous ODEs. IWMM/GIAE 2004 EE Xiao-Shan Gao, Christoph M. Hoffmann Wei-Qiang Yang : Solving spatial basic geometric constraint configurations with locus intersection. Computer-Aided Design 36 EE Jimin Wang , Xiao-Shan Gao: An algorithm for solving partial differential parametric systems. Discrete Applied Mathematics 136 EE Arjeh M. Cohen , Xiao-Shan Gao, Nobuki Takayama : Editorial. J. Symb. Comput. 38
Workshop On Automated Deduction In Geometry (ADG'02)
1700 1730, J. Robu geometry theorem proving in the frame of Theorema Project. 1800, Bus leaves for IBIS Hotel. Thursday, September 05
http://www.risc.uni-linz.ac.at/about/conferences/adg2002/adg02-program.html

Extractions: Bus leaves from IBIS Hotel Opening of the Workshop D. Scott Introducing more abstract algebraic proofs in projective geometry Coffee Break L. Yang Distance coordinates used in geometric constraint solving Testing the normal crossing property of hypersurfaces J. C. Owen, S. C. Power The nonsolvability by radicals of generic 3-connected planar graphs Lunch Break Z. Zeng, H. Fu Subresultants and discriminant sequences I. J. Tchoupaeva H. Li Algebraic representation, expansion and simplification in automated geometric theorem proving Coffee Break X. S. Gao, Q. Lin MMP/Geometer - A software package for Automated Geometric Reasoning - A progress report The SymbolicData Proof Scheme Collection as a multiplatform project J. Robu Geometry theorem proving in the frame of Theorema Project Bus leaves for IBIS Hotel
Foundations Of Geometry: Theorem 3
Theorem 3. If A and C are two points, there exists a point between A and C. Jeff s 1979 Notes. I. Given points A and C, line AC also exists Axiom III.
http://www.doublebit.com/archives/math/sstp1979/foundations/theorem3.htm

Extractions: If A and C are two points, there exists a point between A and C. I. Given points A and C, line AC also exists [ Axiom III II. There is a point D not contained in line AC [ Axiom II III. There is also a point E such that CDE [ Axiom IV IV. Similarly, there is also a point F such that AEF [ Axiom IV again]. V. Since A, E, and C are non-collinear, and both AEF and CDE exist, there is a point B such that FDB and ABC [ Axiom IX ]. B is a point between A and C. [I made a note in the margin: "Why are A, E, and C non-collinear?"]
Foundations Of Geometry: Theorem 2
In other words, we re going to hypothesize that Theorem 2 is false and show that leads to a III. Since the hypothesis is false, Theorem 2 must be true.
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.
GEOTHER - Geometry Theorem Prover
GEOTHER (geometry theorem provER), a module of Epsilon, is an environment implemented by Dongming Wang in Maple with drawing routines and interface written
http://www-calfor.lip6.fr/~wang/GEOTHER/

Extractions: Version 1.0 GEOTHER (GEOmetry THeorem provER), a module of Epsilon , 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 used for 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 or Chinese 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 and modified with a mouse click and dragging, and saved as PostScript files; prove the theorem using any of the five algebraic provers;
GEOTHER - Geometry Theorem Prover
GEOTHER (geometry theorem provER) is an environment implemented by Dongming Wang in Maple with drawing routines and interface written previously in C and
http://www-calfor.lip6.fr/~wang/epsilon/GEOTHER/

Extractions: Version 1.0 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 used for 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 or Chinese 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 and modified with a mouse click and dragging, and saved as PostScript files; prove the theorem using any of the five algebraic provers;

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