User Manual for the Interactive Geometry Software Cinderella

154 Pages·2000·8.734 MB·English

by  Jürgen Richter-Gebert, Ulrich H. Kortenkamp (auth.)

Richter-Gebert • Kortenkamp
•
User Manual
for the Interactive Geometry Software
Cinderella
Springer-Verlag Berlin Heidelberg GmbH
Jürgen Richter-Gebert
Ulrich H. Kortenkamp
User Manual
for the Interactive
Geometry Software
Cinderella
With 126 Figures
mm Springer
Jürgen Richter-Gebert Ulrich H. Kortenkamp
Institut für Theoretische Informatik Institut für Informatik
ETH Zentrum Freie Universität Berlin
8092 Zürich, Switzerland Takustraße 9
email: 14195 Berlin, Germany
[email protected] email:
[email protected] [email protected]
[email protected]
Additional material to this book can be downloaded from http://extra.springer.com.
This book is except for some minor corrections identical with the book published together with the
CD-ROM in 1999 under the title: The Interactive Geometry Software Cinderella
ISBN 978-3-540-67139-8 ISBN 978-3-642-58318-6 (eBook)
DOI 10.1007/978-3-642-58318-6
Library of Congress Cataloging-in-Publication Data
Richter-Gebert, Jürgen, 1963-. User manual for the interactive geometry software, Cinderella / Jürgen
Richter-Gebert, Ulrich H. Kortenkamp.
p. cm. Includes bibliographical references. ISBN 3540671390 (softcover : alk. paper)
1. Geometry-Data processing. 2. Cinderella (Computer file) I. Kortenkamp, Ulrich H.
QA448.D38 R53 2000 5i6\oo285'2369-dc2i 00-039470
Mathematics Subject Classification (2000): 51-04
ISBN 978-3-540-67139-8
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is
concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcast
ing, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this
publication or parts thereof is permitted only under the provisions of the German Copyright Law of
September 9, 1965, in its current version, and permission for use must always be obtained from
Springer-Verlag. Violations are liable for prosecution under the German Copyright Law.
© Springer-Verlag Berlin Heidelberg 2000
Originally published by Springer-Verlag Berlin Heidelberg New York in 2000
The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of
a specific statement, that such names are exempt from the relevant protective laws and regulations and
therefore free for general use.
Please note: All rights pertaining to the Software (program and handbook) are owned exclusively by
the authors and Springer-Verlag. The software is protected by copyright. The publisher and the authors
accept no legal responsibility for any damage caused by improper use of the instructions and programs
contained in this book and the CD-ROM. Although the software has been tested with extreme care, er
rors in the software cannot be excluded. Decompiling, disassembling, reverse engineering or in any way
changing the program is expressly forbidden. For more details concerning the conditions of use and
warranty we refer to the License Agreement in this book (pp. i3iff.).
Legal note: Java and all Java-based trademarks and logos are trademarks or registered trademarks of
Sun Microsystems, Inc. in the United States and other countries. Springer-Verlag and the authors are
independent of Sun. For details concerning the Java Runtime Environment license see Sect. 8.3,
pp. i39ff. All other brand and product names are trademarks, registered trademarks or service marks
of their respective holders.
Awards: Multimedia-Transfer '97: Most innovative Multimedia software
Finalist of the European Academic Software Award (EASA) 1998
Photocomposed from the authors' HTML file.
Cover design: design & production, Heidelberg
Printed on acid-free paper SPIN 10760652 46/3143K0 - 5 4 3 2 1 0
Contents
1 Preface.
2 Introduction 3
2.1 Sample Applications 4
2.1.1 Exact Drawings 4
2.1.2 Geometric Calculator . 5
2.1.3 Student Exercises 5
2.2 Design and Features . 6
2.3 Technical Background 9
3 A Quick Start 11
3.1 Pappos' Theorem 12
3.1.1 Drawing Your First Point 12
3.1.2 Undoing an Operation 13
3.1.3 Moving a Point 13
3.1.4 Adding a Line 14
3.1.5 Adding More Lines 14
3.1.6 Creating Points of Intersection. 15
3.1.7 Finishing the Drawing 16
3.1.8 Selecting and Changing the Appearance 16
3.1.9 Adding a Final Point and Proving a Theorem 18
3.1.10 Moving Points to Infinity 19
3.2 A Three Bar Linkage . 22
3.2.1 Making a Bar 22
3.2.2 Adding Two More Bars 23
3.2.3 Moving the Construction 25
3.2.4 Starting an Animation 26
3.2.5 Drawing a Locus. 26
vi Contents
4 Behilld the Scenes 29
4.1 Probl m in Interactive Geometry 29
4.1. I Static Problems . 29
4.1.2 Dynamic Problems 30
4.2 Projective Geom try . 32
4.3 Homogelleoll Coordinates 33
4.4 omplex umber 35
4.5 Measurements and Complex umbers 38
4.5.1 Euclidean and on-euclidean Geom try 38
4.5.2 Cayley-Klein Geometries 39
4.6 The Principle of onLilluity 42
5 Reference 45
5.1 Overview 45
5.1.1 The Menu 46
5.1.2 The General Action Toolbar 46
5.1.3 The Geometric Tools 47
5.1.4 The G m tries 48
5.1.5 Th Vi w. 48
5.2 General Tools 49
5.2. I ile Operation 49
1-11
5.2.1.1 New 49
~
5.2.1.2 Load 49
~
5.2.1.3 Save 49
~
5.2.1.4 Sav s 49
5.2.2 xport Tools 49
5.2.2.1 I ~ Print All Views 49
~
5.2.2.2 xport to HTML 49
[;l)1
5.2.2.3 Create an Exercis 50
5.2.3 ndolRedo . 50
Contents vii
~
5.2.3.1 ndo 50
Q
5.2.3.2 Redo 50
r::d"
5.2.3.3 Delete 50
5.2.4 Selecrtiuon Tools 50
5.2.4.1 Select All 50
~
5.2.4.2 1l..:.J Select Point 51
!Wi
5.2.4.3 Select Line 51
5.2.4.4 ru Select ni 51
5.2.4.5 De elect 51
5.2.5 Moving an Element 52
5.2.6 ' Select. 54
5.2.7 Intermactive Mod s 55
5.2.7.1 Add a Point. 56
5.2.7.2 . Add a Line. 58
5.2.7.3 'Lin Through Point 60
~
5.2.7.4 Add a Parallel 61
~
5.2.7.5 Add a Perpendicular . 63
~
5.2.7.6 Add a Line With ixed Angle. 64
5.2.7.7 10 J Add a Circle 65
5.2.7.8 1.8 J Circle by Radius 66
~
5.2.7.9 Circle by Fi ed Radiu 67
Ib~· ~~
5.2.7.10 Midpoint 68
5.2.8 Definition Modes 69
10
5.2.8.1 • Center . . . 71
ruM
5.2.8.2 l~ Angular Bisector 72
I )J
5.2.8.3 Compas 73
~
5.2.8.4 ;: . Mirror . 74
[Ql
5.2.8.5 Circle by Three Point 75
viii Contents
IQ1
5.2.8.6 onic by Five Points 76
~
5.2.8.7· Polar of a Point 77
~
5.2.8.8 Polar of a Line 78
I< 11
5.2.8.9 Polygon 79
Ia
5.2.8.10 Join 80
\>
5.2.8.1 I Me t 81
~
5.2.8.12 Define a Parallel 82
I2LI
5.2.8.13 Define a Perpendicular 83
5.2.9 Mea urement 84
~
5.2.9.1 I~ Di tance 85
~
5.2.9.2 Angle 86
I
5.2.9.3 (jj-Area 87
5.2.10 pecial Mode 88
i
5.2.10.1 ABC-Add Text 88
~
5.2.1 0.2 Locus. 90
5.2.10.3 Animation. 92
r:.Al
5.2. J 0.4 I~ Add a Segment 94
.3 Geomelries 96
5.3.1 Types of Geomelrie. 96
5.3.2 View and Geometrie. 98
SA Th Views 99
504.1 Euclidean View 99
GEl
5.4.1.1 Translate 99
I~ .
5.4.1.2 , Zoom In 100
EJ
5.4.1.3 Zoom out 100
5.4.1.4 . Toggle Grid 100
E..:!2
5.4.1.5 Toggi Axes 100
~
5.4.1.6 Toggle Snap 100
Contents ix
5.4.1.7 + Dens r Grid 101
5.4.1.8 oarser Grid 101
5.4.2 Spherical View 101
5.4.2.1 102
5.4.2.2 Spherical Re et 102
5.4.2.3 The Scale Slider 103
5.4.3 Hyperbolic View. 103
5.4.4 Polar Euclidean and Spheri al Vi w 103
5.4.5 Construction Text 104
5.4.6 General unction. 105
~
5.4.6.1 Generate PostScript 106
I
5.4.6.2 Euc Hyp I Ell Choo e the Geometry 106
5.5 The App arance Editor 107
5.~.1 Color 108
5.5.2 View Colors . 109
5.5.3 Clipping 110
5.5.4 Labelling III
5.5.5 Pinning III
5.5.6 Overhang 112
5.5.7 Size 112
5.5.8 Opaquenes' 113
6 Creating Interactive Wehpages and Exercises 114
6.1 Glos 'ary 114
6.2 xporting Plain Examples. 115
6.3 Exporting nimations 116
6.4 Creating Interactive. xerci' S 117
6.4.1 Exercise onstruction 117
6.4.2 Editing the xercise . 118
6.4.2.1 Defining the Input 118
x Contents
6.4.2.2 Defining Solutions 120
6.4.2.3 Defining Hints 121
6.4.2.4 Tool Selection 123
6.4.3 Saving and Creating the HTML 123
6.4.4 Testing the Exercise . 124
6.4.5 Design Considerations 124
6.5 Post-Processing 125
6.6 Legal Issues . 126
7 Installation . 127
7.1 General Information 127
7.2 Installing on Windows 95, 98 or NT 4.0 127
7.3 Installation on Unix Platforms. 128
7.3.1 Installing on Sun Solaris (SPARC) . 128
7.3.2 Other Unix-like Platforms. 128
7.3.3 Installing a JVM on Linux 128
7.4 Installing on MacOS . 129
7.5 Installing on Other Java Platforms 129
7.6 Installing Using a Web Browser 129
7.7 Troubleshooting . 130
7.8 Installing Netscape 130
8 License Agreement . 131
8.1 Conditions of Use and Terms of Warranty 131
8.2 Nutzungs- und Garantiebedingungen 135
8.3 Java(tro) Runtime Environment 139
9 References . 142