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Titlebook: Exploring Classical Greek Construction Problems with Interactive Geometry Software; Ad Meskens,Paul Tytgat Book 2017 Springer Internationa

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发表于 2025-3-21 17:28:23 | 显示全部楼层 |阅读模式
书目名称Exploring Classical Greek Construction Problems with Interactive Geometry Software
编辑Ad Meskens,Paul Tytgat
视频video
概述This book is the first to apply Interactive Geometry Software to classic Greek construction problems in a didactical, enquiry based approach.The history of classic Greek construction problems explored
丛书名称Compact Textbooks in Mathematics
图书封面Titlebook: Exploring Classical Greek Construction Problems with Interactive Geometry Software;  Ad Meskens,Paul Tytgat Book 2017 Springer Internationa
描述In this book the classical Greek construction problems are explored in a didactical, enquiry based fashion using Interactive Geometry Software (IGS). The book traces the history of these problems, stating them in modern terminology. By focusing on constructions and the use of IGS the reader is confronted with the same problems that ancient mathematicians once faced. The reader can step into the footsteps of Euclid, Viète and Cusanus amongst others and then by experimenting and discovering geometric relationships far exceed their accomplishments. Exploring these problems with the neusis-method lets him discover a class of interesting curves..By experimenting he will gain a deeper understanding of how mathematics is created. More than 100 exercises guide him through methods which were developed to try and solve the problems. The exercises are at the level of undergraduate students and only require knowledge of elementary Euclidean geometry and pre-calculus algebra. It is especially well-suited for those students who are thinking of becoming a mathematics teacher and for mathematics teachers..
出版日期Book 2017
关键词Delian problem; straightedge and compass; ruler and compass; GeoGebra; neusis; circle quadrature; duplicat
版次1
doihttps://doi.org/10.1007/978-3-319-42863-5
isbn_softcover978-3-319-42862-8
isbn_ebook978-3-319-42863-5Series ISSN 2296-4568 Series E-ISSN 2296-455X
issn_series 2296-4568
copyrightSpringer International Publishing Switzerland 2017
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发表于 2025-3-21 22:11:54 | 显示全部楼层
https://doi.org/10.1007/978-1-4842-5473-8omplished with compass and straightedge methods, but other geometrical constructions are possible..We now know that the area of a circle is given by .. Now suppose that a square with edge . has the same area. Then ., from which .. The problem of squaring the circle is thereby reduced to constructing
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Squaring the circle,omplished with compass and straightedge methods, but other geometrical constructions are possible..We now know that the area of a circle is given by .. Now suppose that a square with edge . has the same area. Then ., from which .. The problem of squaring the circle is thereby reduced to constructing
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PL/SQL Optimization Techniques,ses, these are exercises whose history goes back to Ancient Greece..We explore two of Plato’s construction categories: constructions with conic sections and constructions with mechanical aids, with historic examples (van Roomen, Viète, van Schooten). In particular neusis or verging constructions are
发表于 2025-3-22 17:39:01 | 显示全部楼层
Relational Database Systems and Oracle,ghtedge constructions. In this chapter we take a closer look at some elementary and not so elementary constructions, culminating is a discussion of Viète’s construction of a circle tangent to three given circles.
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https://doi.org/10.1007/0-387-33530-7 equal parts, by compass and straightedge methods then comes naturally..The question is simple enough and seems to suggest a simple solution. Here too, appearances are deceptive. It turns out that, like the duplication of the cube, the construction with compass and straightedge is impossible. We can
发表于 2025-3-23 07:34:15 | 显示全部楼层
https://doi.org/10.1007/978-1-4842-5473-8same area as a given figure. We still refer to the square root of a number, meaning we are looking for the length of the edge of a square with the given number as area..‘‘Squaring the circle’’ has become more or less a catch line for something which is impossible or unsolvable. Indeed, the problem c
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