基于网络数据共享的平面几何自动推理系统的研究
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摘要
平面几何自动推理系统是利用计算机软件开发技术,将数学机械化领域中定理机器证明的几何自动推理的研究成果转化为软件的产物。平面几何自动推理系统目前主要应用在数学教育方面,它使教育软件变得智能化,它的出现具有深刻的理论和实际意义。平面几何是初中数学中的重要内容,学习它可以锻炼学生的思维,提高学生的能力,在学生的成长中有重要作用。平面几何自动推理系统为教师和学生学习平面几何知识、研究平面几何问题提供了一个现代化的工具,教师可以使用它辅助教学,创新试题,启发与调动学生发散思维,学生可以使用它进行研究性学习。
当前的平面几何自动推理软件基本都是单机软件,存在着一定的局限性。本文着眼于当前软件与互联网的发展趋势,根据相关的学习理论,研究如何在网络环境下给教师和学生提供方便快捷的动态几何以及自动推理服务。具体来说,本文基于Silverlight和Asp.Net研究了如何在浏览器中实现动态几何、推理的输入与呈现；研究了在网络环境中传递系统所需的各种图形及推理数据的方式；研究了在服务器运行的平面几何自动推理引擎；研究了图形及推理数据的网络共享机制。根据这些研究的结果开发实现了一个基于网络数据共享的平面几何自动推理系统的模型,并在模型中实现了两个较为实用的教学应用。
本文的研究,为具有自动推理功能的网络平面几何软件的开发提供了切实可行的方法和参照。
Geometry automated reasoning system is the commercialization of geometry automated reasoning method in mathematics mechanization by using computer software development technology. Geometry automated reasoning systems are mainly used in mathematics education, it makes educational software become intelligent, its emergence has profound theoretical and practical significance. Plane geometry is an important part of middle school mathematics, learning it can exercise the students'thinking, improve students'ability, it plays an important role in the growth of students. Geometry automated reasoning system provides a modern tool for teachers and students to study the problem of plane geometry,teachers can use it to facilitate teaching, innovative questions, inspire and mobilize students to divergent thinking, students can use it for inquiry learning.
The current geometry software mostly is old software, which have some limitations. This thesis, focusing on the current trends of software industry and internet, according to related learning theory, study how to provide dynamic geometry and automated reasoning services conveniently for teachers and students under the network environment. To be more specific, this study based on Asp.Net and Silverlight, study how to implement dynamic geometry, input and presence reasoning, study how to transfer figure and reasoning data in internet, study reasoning engine which run at sever, study how to share figure and reasoning data. According to the results of these studies, we developed a demo software of plane geometry automated reasoning system based on web data sharing, which have two useful teaching application
This study provides some methods and references for developing network plane geometry software which have automated reasoning function.
当前的平面几何自动推理软件基本都是单机软件,存在着一定的局限性。本文着眼于当前软件与互联网的发展趋势,根据相关的学习理论,研究如何在网络环境下给教师和学生提供方便快捷的动态几何以及自动推理服务。具体来说,本文基于Silverlight和Asp.Net研究了如何在浏览器中实现动态几何、推理的输入与呈现；研究了在网络环境中传递系统所需的各种图形及推理数据的方式；研究了在服务器运行的平面几何自动推理引擎；研究了图形及推理数据的网络共享机制。根据这些研究的结果开发实现了一个基于网络数据共享的平面几何自动推理系统的模型,并在模型中实现了两个较为实用的教学应用。
本文的研究,为具有自动推理功能的网络平面几何软件的开发提供了切实可行的方法和参照。
Geometry automated reasoning system is the commercialization of geometry automated reasoning method in mathematics mechanization by using computer software development technology. Geometry automated reasoning systems are mainly used in mathematics education, it makes educational software become intelligent, its emergence has profound theoretical and practical significance. Plane geometry is an important part of middle school mathematics, learning it can exercise the students'thinking, improve students'ability, it plays an important role in the growth of students. Geometry automated reasoning system provides a modern tool for teachers and students to study the problem of plane geometry,teachers can use it to facilitate teaching, innovative questions, inspire and mobilize students to divergent thinking, students can use it for inquiry learning.
The current geometry software mostly is old software, which have some limitations. This thesis, focusing on the current trends of software industry and internet, according to related learning theory, study how to provide dynamic geometry and automated reasoning services conveniently for teachers and students under the network environment. To be more specific, this study based on Asp.Net and Silverlight, study how to implement dynamic geometry, input and presence reasoning, study how to transfer figure and reasoning data in internet, study reasoning engine which run at sever, study how to share figure and reasoning data. According to the results of these studies, we developed a demo software of plane geometry automated reasoning system based on web data sharing, which have two useful teaching application
This study provides some methods and references for developing network plane geometry software which have automated reasoning function.
引文
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[2]Tabak,J.Geometry:The Language of Space and Form[M].New York:Facts on File,2004:1.
[3]徐章韬.师范生面向教学的数学知识之研究[D].上海：华东师范大学博士论文,2009：117.
[4]中国互联网络信息中心,第25次中国互联网络发展状况统计报告[R]北京：中国互联网络信息中心,2010：10,61.
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[10]张景中.动态几何教程[M].北京：科学出版社,2007：1.
[11]Sutherland,I.E. Sketchpad:A man-machine graphical communication system[R]. London: University of Cambridge Computer Laboratory,2003.
[12]江建国.iGeo智能几何软件的定理证明器[D].成都：中国科学院成都计算机应用研究所博士论文,2006：摘要.
[13]GCLC[CP/OL].http://www.matf.bg.ac.yu/-janicic/gclc/,2009-5-7.
[14]GeoProof[CP/OL].http://home.gna.org/geoproof/,2009-05-08.
[15]Geometrix[CP/OL].http://geometrix.free.fr/geom3exos/,2009-5-9.
[16]Dynamic geometry[CP/OL].http://geometry.osenkov.com/,2009-05-21.
[17]GeometryEditor[CP/OL].http://boar.cs.kent.edu/geosite/editman.php?id=/testerl & tool= GeometryEditor,2009-5-22.
[18]Java Geometry Expert[CP/OL]..http://www.cs.wichita.edu/-ye/index.html,2009-5-22.
[19]Hilbert D. The Foundations of Geometry [M]. London:Prentice Hall,2006:35.
[20]黄勇.基于前推能产生传统证明的几何自动解题系统[D].成都：四川大学博士论文,1999：1-5.
[21]Tariski,A.A decision method for elementary algebra and geometry[M].Santa Monic:The RAND Corporarion,1949:108.
[22]吴文俊.初等几何判定问题与证明机械化[J],中国科学,1977,6：507-516.
[23]张景中,高小山,周咸青.基于前推法的几何信息搜索系统[J].计算机学报,1996,19(10)：721-727.
[24]张景中.计算机怎样解几何题——谈谈自动推理[M].广州,北京：清华大学出版社,暨南大学出版社,2000：23.
[25]Wenjun.W,Xiaoshan.G.Mathematics mechanization and applications after thirty years[J]. Frontiers of Computer Science in China,2007,1(1):1-8.
[26]张景中,李永彬.几何定理机器证明三十年[J].系统科学与数学,2009,29(9)：1155-1168.
[27]YongBin,L.,Wu,L.&XiaoLin,Xia. Geometry theorems proving by decomposing polynomial systems into strong regular sets[J]. Journal of Computer Science and Technology,2004, 19(6):820-827.
[28]徐茜.双向推理系统在初等几何自动解题中的实现[J].计算机应用研,2004(11)：232-234.
[29]郭四稳.基于用户自添加规则的自动推理程序[J].计算机应用与软件,2007(9)：48-50.
[30]郭四稳.基于用户自添加规则的自动推理程序Ⅱ[J].计算机与信息技术,2006(8)：61-71.
[31]邹宇,付云皓,张景中.几何代数基础新视角下的初步探讨[J].系统科学与数学,2010,30(1)：1-11.
[32]张景中,李传中.自动推理与教育软件智能平台[J].广州大学学报(综合版),2001(2)：1-6.
[33]Govindasamy,T. Successful implementation of e-learning pedagogical considerations[J]. The Internet and Higher Education,2002(4):287-299.
[34]Sanderson,P.E,E-Learning:strategies for delivering knowledge in the digital age[J]. Internet and Higher Education,2002(5):185-188.
[35].Richard W. Riley. E-Learning:putting a World Class Education at the Fingertips of All Children [M]. Washington, D. C:Department of Education, Office of Educational Technology,2000:89.
[36]Darian,S. Preparing for blended e-Learning[J].Technical Communication,2008,55(3): 285-287.
[37]董宏建.网络环境下教师跨学科协作学习研究[D]上海：华东师范大学博士论文,2008：9.
[38]庞国斌,王冬凌.合作学习的理论与实践[M].北京：开明出版社,2003：26-27.
[39]Johnson,D.W., & Johnson,R.T.Learning together and alone:Cooperative competitive and individualistic learning[M].Boston:Allyn and Bacon,1999:91.
[40]Stahl, Q., Koschmann,T., & Suthers,D. Computer-Supported Collaborative Learning:An Historical Perspective[A].Cambridge Handbook of the Learning Sciences,2006:409-426.
[41]Garrison,D. R.,Anderson,T., & Archer,W. Critical inquiry in a text-based environment: Computer conferencing in higher education[J]. The Internet and Higher Education,1999(2): 87-105.
[42]柯清超.面向混合学习的教师教育技术能力培训模式研究[J].电化教育研究,2008(2)：58-62.
[43]Picciano,A.G. Blended leaming:Implicafions for growth and access[J]. Journal of Asynchronous Learning Networks,2006(3):95-102.
[44]Driscoll,M.Blended Learning:Let's Get Beyond the Hype[R/OL].http://www-07.ibm.com/ services/pdf/blended_learning.pdf,2009-6-1
[45]MacDonald,M.Pro Silverlight 2 in c# 2008[M] New Yorks:Springer-Verlag,2009 (xxiii).
[46]Silverlight Overview [EB/OL].http://msdn.microsoft.com/en-us/library/bb404700(v=VS.9 5).aspx,2009-6-8.
[47]Silverlight Architecture [EB/OL].http://msdn.microsoft.com/en-us/library/bb404713(v=VS.9 5).aspx,2009-6-8.
[48]Juval,L.Programming WCF Services[M].Sebastopol:O'Reilly Media 2007:309.
[49]Windows Communication Foundation[EB/OL].http://msdn.microsoft.com/zh-cn/library/ms 731079.aspx,2009-9-2.
[50]LINQ to SQL[EB/OL].http://msdn.microsoft.com/en-us/library/bb386976.aspx,2009-9-8.
[51]Silverlight Databind[EB/OL]. http://msdn.microsoft.com/en/library/cc278072%28VS.95%2 9.aspx,2009-9-10.
[52]Dynamic Geometry Module:What Is Dynamic Geometry? [EB/OL] http://mtl.math.uiuc.e du/modules/dynamic/lessons/lessonl.html,2009-9-12.
[2]Tabak,J.Geometry:The Language of Space and Form[M].New York:Facts on File,2004:1.
[3]徐章韬.师范生面向教学的数学知识之研究[D].上海：华东师范大学博士论文,2009：117.
[4]中国互联网络信息中心,第25次中国互联网络发展状况统计报告[R]北京：中国互联网络信息中心,2010：10,61.
[5]刘颖奇,黄勇.几何自动推理系统发展研究[J].山西广播电视大学学报,2010,3.
[6]google documents[CP/OL].http://docs.google.com/,2010-3-12
[7]Peter.K.Global Netbook Vendor Market Share:2009[EB/OL].http://www.strategyanalytics. com/default.aspx?mod=ReportAbstractViewer&a0=5272,2010-03-13.
[8]09年上网本出货量3020万部占便携PC20%[EB/OL]. http://www.ccgp.gov.cn/gysh/itch/ schq/1108521.shtml,2010-2-10.
[9]Crowder,N.A,Automatic Tutoring by Means of Intrinsic Programming[A]. E. H. Galatiter. Automatic Teaching:The State of the Art[C]. Washington, D. C.:Department of Audio visual Instruction, National Education Association 1960:301-302.
[10]张景中.动态几何教程[M].北京：科学出版社,2007：1.
[11]Sutherland,I.E. Sketchpad:A man-machine graphical communication system[R]. London: University of Cambridge Computer Laboratory,2003.
[12]江建国.iGeo智能几何软件的定理证明器[D].成都：中国科学院成都计算机应用研究所博士论文,2006：摘要.
[13]GCLC[CP/OL].http://www.matf.bg.ac.yu/-janicic/gclc/,2009-5-7.
[14]GeoProof[CP/OL].http://home.gna.org/geoproof/,2009-05-08.
[15]Geometrix[CP/OL].http://geometrix.free.fr/geom3exos/,2009-5-9.
[16]Dynamic geometry[CP/OL].http://geometry.osenkov.com/,2009-05-21.
[17]GeometryEditor[CP/OL].http://boar.cs.kent.edu/geosite/editman.php?id=/testerl & tool= GeometryEditor,2009-5-22.
[18]Java Geometry Expert[CP/OL]..http://www.cs.wichita.edu/-ye/index.html,2009-5-22.
[19]Hilbert D. The Foundations of Geometry [M]. London:Prentice Hall,2006:35.
[20]黄勇.基于前推能产生传统证明的几何自动解题系统[D].成都：四川大学博士论文,1999：1-5.
[21]Tariski,A.A decision method for elementary algebra and geometry[M].Santa Monic:The RAND Corporarion,1949:108.
[22]吴文俊.初等几何判定问题与证明机械化[J],中国科学,1977,6：507-516.
[23]张景中,高小山,周咸青.基于前推法的几何信息搜索系统[J].计算机学报,1996,19(10)：721-727.
[24]张景中.计算机怎样解几何题——谈谈自动推理[M].广州,北京：清华大学出版社,暨南大学出版社,2000：23.
[25]Wenjun.W,Xiaoshan.G.Mathematics mechanization and applications after thirty years[J]. Frontiers of Computer Science in China,2007,1(1):1-8.
[26]张景中,李永彬.几何定理机器证明三十年[J].系统科学与数学,2009,29(9)：1155-1168.
[27]YongBin,L.,Wu,L.&XiaoLin,Xia. Geometry theorems proving by decomposing polynomial systems into strong regular sets[J]. Journal of Computer Science and Technology,2004, 19(6):820-827.
[28]徐茜.双向推理系统在初等几何自动解题中的实现[J].计算机应用研,2004(11)：232-234.
[29]郭四稳.基于用户自添加规则的自动推理程序[J].计算机应用与软件,2007(9)：48-50.
[30]郭四稳.基于用户自添加规则的自动推理程序Ⅱ[J].计算机与信息技术,2006(8)：61-71.
[31]邹宇,付云皓,张景中.几何代数基础新视角下的初步探讨[J].系统科学与数学,2010,30(1)：1-11.
[32]张景中,李传中.自动推理与教育软件智能平台[J].广州大学学报(综合版),2001(2)：1-6.
[33]Govindasamy,T. Successful implementation of e-learning pedagogical considerations[J]. The Internet and Higher Education,2002(4):287-299.
[34]Sanderson,P.E,E-Learning:strategies for delivering knowledge in the digital age[J]. Internet and Higher Education,2002(5):185-188.
[35].Richard W. Riley. E-Learning:putting a World Class Education at the Fingertips of All Children [M]. Washington, D. C:Department of Education, Office of Educational Technology,2000:89.
[36]Darian,S. Preparing for blended e-Learning[J].Technical Communication,2008,55(3): 285-287.
[37]董宏建.网络环境下教师跨学科协作学习研究[D]上海：华东师范大学博士论文,2008：9.
[38]庞国斌,王冬凌.合作学习的理论与实践[M].北京：开明出版社,2003：26-27.
[39]Johnson,D.W., & Johnson,R.T.Learning together and alone:Cooperative competitive and individualistic learning[M].Boston:Allyn and Bacon,1999:91.
[40]Stahl, Q., Koschmann,T., & Suthers,D. Computer-Supported Collaborative Learning:An Historical Perspective[A].Cambridge Handbook of the Learning Sciences,2006:409-426.
[41]Garrison,D. R.,Anderson,T., & Archer,W. Critical inquiry in a text-based environment: Computer conferencing in higher education[J]. The Internet and Higher Education,1999(2): 87-105.
[42]柯清超.面向混合学习的教师教育技术能力培训模式研究[J].电化教育研究,2008(2)：58-62.
[43]Picciano,A.G. Blended leaming:Implicafions for growth and access[J]. Journal of Asynchronous Learning Networks,2006(3):95-102.
[44]Driscoll,M.Blended Learning:Let's Get Beyond the Hype[R/OL].http://www-07.ibm.com/ services/pdf/blended_learning.pdf,2009-6-1
[45]MacDonald,M.Pro Silverlight 2 in c# 2008[M] New Yorks:Springer-Verlag,2009 (xxiii).
[46]Silverlight Overview [EB/OL].http://msdn.microsoft.com/en-us/library/bb404700(v=VS.9 5).aspx,2009-6-8.
[47]Silverlight Architecture [EB/OL].http://msdn.microsoft.com/en-us/library/bb404713(v=VS.9 5).aspx,2009-6-8.
[48]Juval,L.Programming WCF Services[M].Sebastopol:O'Reilly Media 2007:309.
[49]Windows Communication Foundation[EB/OL].http://msdn.microsoft.com/zh-cn/library/ms 731079.aspx,2009-9-2.
[50]LINQ to SQL[EB/OL].http://msdn.microsoft.com/en-us/library/bb386976.aspx,2009-9-8.
[51]Silverlight Databind[EB/OL]. http://msdn.microsoft.com/en/library/cc278072%28VS.95%2 9.aspx,2009-9-10.
[52]Dynamic Geometry Module:What Is Dynamic Geometry? [EB/OL] http://mtl.math.uiuc.e du/modules/dynamic/lessons/lessonl.html,2009-9-12.
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