Rethinking proof with The Geometer's Sketchpad:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Emmeryville, CA
Key Curriculum Press
2006
|
| Edition: | [Nachdr.], Sketchpad version 4 ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 214 S. Ill., graph. Darst. 1 CD-ROM (12 cm) |
| ISBN: | 1559536462 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Titel: Rethinking proof with The Geometer s Sketchpad
Autor: De Villiers, Patrice
Jahr: 2006
CONTENTS
Introduction.....................................................1
Chapter 0: The Role of Proof.......................................3
The Role and Function of Proof with Sketchpad.....................5
The van Hiele Theory—Defining and Proving Within a
Sketchpad Context.............................................11
Chapter 1: Proof as Explanation...................................21
Distances in an Equilateral Triangle...............................23
Water Supply I: Four Towns.....................................27
Water Supply II: Three Towns ...................................31
Triangle Angle Sum............................................34
Quadrilateral Angle Sum........................................37
Crossed Quadrilateral Sum......................................40
Isosceles Trapezoid.............................................45
Cyclic Quadrilateral............................................48
The Center of Gravity of a Triangle...............................51
Chapter 2: Proof as Discovery.....................................57
Kite Midpoints................................................59
Logical Discovery .............................................63
Isosceles Trapezoid Midpoints...................................65
Logical Discovery: Circum Quad.................................68
Chapter 3: Proof as Verification ...................................71
Areas........................................................73
Varignon Area.................................................76
Logical Paradox ...............................................80
Cyclic Quadrilateral Converse ...................................82
Concurrency..................................................85
Triangle Altitudes..............................................86
Light Ray in a Triangle..........................................90
Parallel Lines..................................................95
Chapter 4: Proof as Challenge.....................................99
Parallelogram Angle Bisectors ..................................101
Parallelogram Squares.........................................104
The Fermat-Torricelli Point ....................................108
Airport Problem..............................................115
Napoleon ...................................................119
Miquel......................................................122
Rethinking Proof vii
© 2003 Key Curriculum Press
Chapter 5: Proof as Systematization...............................127
Reasoning Backward: Triangle Midpoints ........................129
Reasoning Backward: Parallel Lines..............................131
Systematizing Rhombus Properties ..............................133
Systematizing Isosceles Trapezoid Properties ......................139
Teacher Notes..................................................147
References.....................................................212
viii
Rethinking Proof
© 2003 Key Curriculum Press
|
| any_adam_object | 1 |
| author | De Villiers, Michael D. |
| author_facet | De Villiers, Michael D. |
| author_role | aut |
| author_sort | De Villiers, Michael D. |
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| building | Verbundindex |
| bvnumber | BV019993097 |
| classification_rvk | SM 613 |
| ctrlnum | (OCoLC)635133584 (DE-599)BVBBV019993097 |
| discipline | Mathematik |
| edition | [Nachdr.], Sketchpad version 4 ed. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T20:10:20Z |
| institution | BVB |
| isbn | 1559536462 |
| language | English |
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| oclc_num | 635133584 |
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| physical | VIII, 214 S. Ill., graph. Darst. 1 CD-ROM (12 cm) |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Key Curriculum Press |
| record_format | marc |
| spelling | De Villiers, Michael D. Verfasser aut Rethinking proof with The Geometer's Sketchpad Michael D. De Villiers [Nachdr.], Sketchpad version 4 ed. Emmeryville, CA Key Curriculum Press 2006 VIII, 214 S. Ill., graph. Darst. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Geometer's Sketchpad (DE-588)4845167-8 gnd rswk-swf Beweis (DE-588)4132532-1 gnd rswk-swf Geometer's Sketchpad (DE-588)4845167-8 s Beweis (DE-588)4132532-1 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013314953&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | De Villiers, Michael D. Rethinking proof with The Geometer's Sketchpad Geometer's Sketchpad (DE-588)4845167-8 gnd Beweis (DE-588)4132532-1 gnd |
| subject_GND | (DE-588)4845167-8 (DE-588)4132532-1 |
| title | Rethinking proof with The Geometer's Sketchpad |
| title_auth | Rethinking proof with The Geometer's Sketchpad |
| title_exact_search | Rethinking proof with The Geometer's Sketchpad |
| title_full | Rethinking proof with The Geometer's Sketchpad Michael D. De Villiers |
| title_fullStr | Rethinking proof with The Geometer's Sketchpad Michael D. De Villiers |
| title_full_unstemmed | Rethinking proof with The Geometer's Sketchpad Michael D. De Villiers |
| title_short | Rethinking proof with The Geometer's Sketchpad |
| title_sort | rethinking proof with the geometer s sketchpad |
| topic | Geometer's Sketchpad (DE-588)4845167-8 gnd Beweis (DE-588)4132532-1 gnd |
| topic_facet | Geometer's Sketchpad Beweis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013314953&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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