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Automated Deduction in Geometry最新文献

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Formalising Geometric Axioms for Minkowski Spacetime and Without-Loss-of-Generality Theorems 闵可夫斯基时空和不损失通用性定理几何公理的形式化
Automated Deduction in Geometry Pub Date : 2021-12-29 DOI: 10.4204/EPTCS.352.13
Richard Schmoetten, Jake E. Palmer, Jacques D. Fleuriot
{"title":"Formalising Geometric Axioms for Minkowski Spacetime and Without-Loss-of-Generality Theorems","authors":"Richard Schmoetten, Jake E. Palmer, Jacques D. Fleuriot","doi":"10.4204/EPTCS.352.13","DOIUrl":"https://doi.org/10.4204/EPTCS.352.13","url":null,"abstract":"This contribution reports on the continued formalisation of an axiomatic system for Minkowski spacetime (as used in the study of Special Relativity) which is closer in spirit to Hilbert's axiomatic approach to Euclidean geometry than to the vector space approach employed by Minkowski. We present a brief overview of the axioms as well as of a formalisation of theorems relating to linear order. Proofs and excerpts of Isabelle/Isar scripts are discussed, with a focus on the use of symmetry and reasoning\"without loss of generality\".","PeriodicalId":127390,"journal":{"name":"Automated Deduction in Geometry","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131319931","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
A New Modeling of Classical Folds in Computational Origami 计算折纸中经典褶皱的一种新模型
Automated Deduction in Geometry Pub Date : 2021-12-29 DOI: 10.4204/EPTCS.352.5
T. Ida, Hidekazu Takahashi
{"title":"A New Modeling of Classical Folds in Computational Origami","authors":"T. Ida, Hidekazu Takahashi","doi":"10.4204/EPTCS.352.5","DOIUrl":"https://doi.org/10.4204/EPTCS.352.5","url":null,"abstract":"This paper shows a cut along a crease on an origami sheet makes simple modeling of popular traditional basic folds such as a squash fold in computational origami. The cut operation can be applied to other classical folds and significantly simplify their modeling and subsequent implementation in the context of computational origami.","PeriodicalId":127390,"journal":{"name":"Automated Deduction in Geometry","volume":"100 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121474850","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Automated Generation of Illustrations for Synthetic Geometry Proofs 自动生成的插图合成几何证明
Automated Deduction in Geometry Pub Date : 2021-12-29 DOI: 10.4204/EPTCS.352.9
Predrag Janičić, Julien Narboux
{"title":"Automated Generation of Illustrations for Synthetic Geometry Proofs","authors":"Predrag Janičić, Julien Narboux","doi":"10.4204/EPTCS.352.9","DOIUrl":"https://doi.org/10.4204/EPTCS.352.9","url":null,"abstract":"We report on a new, simple, modular, and flexible approach for automated generation of illustrations for (readable) synthetic geometry proofs. The underlying proofs are generated using the Larus automated prover for coherent logic, and corresponding illustrations are generated in the GCLC language. Animated illustrations are also supported.","PeriodicalId":127390,"journal":{"name":"Automated Deduction in Geometry","volume":"2257 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130225229","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Automated Theorem Proving in the Classroom 课堂上的自动定理证明
Automated Deduction in Geometry Pub Date : 2021-12-29 DOI: 10.4204/EPTCS.352.6
W. Windsteiger
{"title":"Automated Theorem Proving in the Classroom","authors":"W. Windsteiger","doi":"10.4204/EPTCS.352.6","DOIUrl":"https://doi.org/10.4204/EPTCS.352.6","url":null,"abstract":"We report on several scenarios of using automated theorem proving software in university education. In particular, we focus on using the Theorema system in a software-enhanced logic-course for students in computer science or artificial intelligence. The purpose of using logic-software in our teaching is not to teach students the proper use of a particular piece of software. In contrast, we try to employ certain software in order to spark students' motivation and to support their understanding of logic principles they are supposed to understand after having passed the course. In a sense, we try to let the software act as a logic-tutor, the software is not an additional subject we teach.","PeriodicalId":127390,"journal":{"name":"Automated Deduction in Geometry","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127922092","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Online Generation of Proofs Without Words 在线生成无文字证明
Automated Deduction in Geometry Pub Date : 2021-12-29 DOI: 10.4204/EPTCS.352.10
Alexander Thaller, Z. Kovács
{"title":"Online Generation of Proofs Without Words","authors":"Alexander Thaller, Z. Kovács","doi":"10.4204/EPTCS.352.10","DOIUrl":"https://doi.org/10.4204/EPTCS.352.10","url":null,"abstract":"Understanding geometric relationships with little mathematical knowledge can be challenging for today's students and teachers. A new toolset is introduced that is able to create a proof without words by combining the benefits of the Geometric Deduction Database method (to obtain a readable proof of a geometric statement) and the GeoGebra framework (that makes it possible to export these data as an online applet in a simple way).","PeriodicalId":127390,"journal":{"name":"Automated Deduction in Geometry","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128351941","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Realizations of Rigid Graphs 刚性图的实现
Automated Deduction in Geometry Pub Date : 2021-12-29 DOI: 10.4204/EPTCS.352.2
C. Koutschan
{"title":"Realizations of Rigid Graphs","authors":"C. Koutschan","doi":"10.4204/EPTCS.352.2","DOIUrl":"https://doi.org/10.4204/EPTCS.352.2","url":null,"abstract":"A minimally rigid graph, also called Laman graph, models a planar framework which is rigid for a general choice of distances between its vertices. In other words, there are finitely many ways, up to isometries, to realize such a graph in the plane. Using ideas from algebraic and tropical geometry, we derive a recursive formula for the number of such realizations. Combining computational results with the construction of new rigid graphs via gluing techniques, we can give a new lower bound on the maximal possible number of realizations for graphs with a given number of vertices.","PeriodicalId":127390,"journal":{"name":"Automated Deduction in Geometry","volume":"385 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123630486","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Integrated Circumradius and Area Formulae for Cyclic Pentagons and Hexagons 循环五边形和六边形的积分周半径和面积公式
Automated Deduction in Geometry Pub Date : 2014-07-09 DOI: 10.1007/978-3-319-21362-0_6
Shuichi Moritsugu
{"title":"Integrated Circumradius and Area Formulae for Cyclic Pentagons and Hexagons","authors":"Shuichi Moritsugu","doi":"10.1007/978-3-319-21362-0_6","DOIUrl":"https://doi.org/10.1007/978-3-319-21362-0_6","url":null,"abstract":"","PeriodicalId":127390,"journal":{"name":"Automated Deduction in Geometry","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125408923","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
The Relation Tool in GeoGebra 5 GeoGebra中的关系工具
Automated Deduction in Geometry Pub Date : 2014-07-09 DOI: 10.1007/978-3-319-21362-0_4
Z. Kovács
{"title":"The Relation Tool in GeoGebra 5","authors":"Z. Kovács","doi":"10.1007/978-3-319-21362-0_4","DOIUrl":"https://doi.org/10.1007/978-3-319-21362-0_4","url":null,"abstract":"","PeriodicalId":127390,"journal":{"name":"Automated Deduction in Geometry","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130701995","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 23
Recent Advances in Real Geometric Reasoning 真实几何推理的最新进展
Automated Deduction in Geometry Pub Date : 2014-07-09 DOI: 10.1007/978-3-319-21362-0_3
J. Davenport, M. England
{"title":"Recent Advances in Real Geometric Reasoning","authors":"J. Davenport, M. England","doi":"10.1007/978-3-319-21362-0_3","DOIUrl":"https://doi.org/10.1007/978-3-319-21362-0_3","url":null,"abstract":"","PeriodicalId":127390,"journal":{"name":"Automated Deduction in Geometry","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126344600","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Extension of Simson-Wallace Theorem on Skew Quadrilaterals and Further Properties Simson-Wallace定理在斜四边形上的推广及其进一步性质
Automated Deduction in Geometry Pub Date : 2014-07-09 DOI: 10.1007/978-3-319-21362-0_7
P. Pech
{"title":"Extension of Simson-Wallace Theorem on Skew Quadrilaterals and Further Properties","authors":"P. Pech","doi":"10.1007/978-3-319-21362-0_7","DOIUrl":"https://doi.org/10.1007/978-3-319-21362-0_7","url":null,"abstract":"","PeriodicalId":127390,"journal":{"name":"Automated Deduction in Geometry","volume":"583 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132725651","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
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