Math made visual: creating images for understanding mathematics
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Washington, DC
<<The>> Mathematical Assoc. of America
2006
|
| Series: | Classroom resource materials
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 173 S. Ill., graph. Darst. |
| ISBN: | 9780883857465 0883857464 |
Staff View
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Record in the Search Index
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| adam_text | MATH MADE VISUAL CREATING IMAGES FOR UNDERSTANDING MATHEMATICS CLAUDI
ALSINA UNIVERSITAT POLITECNICA DE CATALUNYA AND ROGER B. NELSEN LEWIS &
CLARK COLLEGE PUBLISHED AND DISTRIBUTED BY THE MATHEMATICAL ASSOCIATION
OF AMERICA CONTENTS INTRODUCTION IX PART I: VISUALIZING MATHEMATICS BY
CREATING PICTURES 1 1 REPRESENTING NUMBERS BY GRAPHICAL ELEMENTS 3 1 .1
SUMS OF ODD INTEGERS 3 1.2 SUMS OF INTEGERS 4 1.3 ALTERNATING SUMS OF
SQUARES 5 1.4 CHALLENGES 6 2 REPRESENTING NUMBERS BY LENGTHS OF SEGMENTS
7 2.1 INEQUALITIES AMONG MEANS 7 2.2 THE MEDIANT PROPERTY 9 2.3 A
PYTHAGOREAN INEQUALITY 10 2.4 TRIGONOMETRIC FUNCTIONS 10 2.5 NUMBERS AS
FUNCTION VALUES 11 2.6 CHALLENGES 12 3 REPRESENTING NUMBERS BY AREAS OF
PLANE FIGURES 13 3.1 SUMS OF INTEGERS REVISITED 13 3.2 THE SUM OF TERMS
IN ARITHMETIC PROGRESSION 14 3.3 FIBONACCI NUMBERS 15 3.4 SOME
INEQUALITIES 15 3.5 SUMS OF SQUARES 17 3.6 SUMS OF CUBES 17 3.7
CHALLENGES 18 4 REPRESENTING NUMBERS BY VOLUMES OF OBJECTS 19 4.1 FROM
TWO DIMENSIONS TO THREE 19 4.2 SUMS OF SQUARES OF INTEGERS REVISITED 20
4.3 SUMS OF TRIANGULAR NUMBERS 21 4.4 A DOUBLE SUM 21 4.5 CHALLENGES 22
XI XII MATH MADE VISUAL 5 IDENTIFYING KEY ELEMENTS 23 5.1 ON THE ANGLE
BISECTORS OF A CONVEX QUADRILATERAL 23 5.2 CYCLIC QUADRILATERALS WITH
PERPENDICULAR DIAGONALS 24 5.3 A PROPERTY OF THE RECTANGULAR HYPERBOLA
25 5.4 CHALLENGES 25 6 EMPLOYING ISOMETRY 27 6.1 THE CHOU PEI SUAN CHING
PROOF OF THE PYTHAGOREAN THEOREM 27 6.2 A THEOREM OF THALES 27 6.3
LEONARDO DA VINCI S PROOF OF THE PYTHAGOREAN THEOREM 28 6.4 THE FERMAT
POINT OF A TRIANGLE 29 6.5 VIVIANI S THEOREM 29 6.6 CHALLENGES 30 7
EMPLOYING SIMILARITY 31 7.1 PTOLEMY S THEOREM 31 7.2 THE GOLDEN RATIO IN
THE REGULAR PENTAGON 32 7.3 THE PYTHAGOREAN THEOREM*AGAIN 33 7.4 AREA
BETWEEN SIDES AND CEVIANS OF A TRIANGLE 33 7.5 CHALLENGES 34 8
AREA-PRESERVING TRANSFORMATIONS 35 8.1 PAPPUS AND PYTHAGORAS 35 8.2
SQUARING POLYGONS 37 8.3 EQUAL AREAS IN A PARTITION OF A PARALLELOGRAM
38 8.4 THE CAUCHY-SCHWARZ INEQUALITY 38 8.5 A THEOREM OF GASPARD MONGE
39 8.6 CHALLENGES 40 9 ESCAPING FROM THE PLANE 43 9.1 THREE CIRCLES AND
SIX TANGENTS 43 9.2 FAIR DIVISION OF A CAKE 44 9.3 INSCRIBING THE
REGULAR HEPTAGON IN A CIRCLE 44 9.4 THE SPIDER AND THE FLY 45 9.5
CHALLENGES 46 10 OVERLAYING TILES 47 10.1 PYTHAGOREAN TILINGS 47 10.2
CARTESIAN TILINGS 49 10.3 QUADRILATERAL TILINGS 50 10.4 TRIANGULAR
TILINGS 51 10.5 TILING WITH SQUARES AND PARALLELOGRAMS 51 10.6
CHALLENGES 52 11 PLAYING WITH SEVERAL COPIES 55 11.1 FROM PYTHAGORAS TO
TRIGONOMETRY 55 11.2 SUMS OF ODD INTEGERS REVISITED 56 CONTENTS XIII
11.3 SUMS OF SQUARES AGAIN 56 11.4 THE VOLUME OF A SQUARE PYRAMID 57
11.5 CHALLENGES 57 12 SEQUENTIAL FRAMES 59 12.1 THE PARALLELOGRAM LAW 59
12.2 AN UNKNOWN ANGLE 61 12.3 DETERMINANTS 61 12.4 CHALLENGES 62 13
GEOMETRIC DISSECTIONS 63 13.1 CUTTING WITH INGENUITY 64 13.2 THE SMART
ALEC PUZZLE 65 13.3 THE AREA OF A REGULAR DODECAGON 66 13.4 CHALLENGES
66 14 MOVING FRAMES 69 14.1 FUNCTIONAL COMPOSITION 69 14.2 THE LIPSCHITZ
CONDITION 70 14.3 UNIFORM CONTINUITY 71 14.4 CHALLENGES 72 15 ITERATIVE
PROCEDURES 73 15.1 GEOMETRIC SERIES 73 15.2 GROWING A FIGURE ITERATIVELY
74 15.3 A CURVE WITHOUT TANGENTS 76 15.4 CHALLENGES 76 16 INTRODUCING
COLORS 79 16.1 DOMINO TILINGS 79 16.2 L-TETROMINO TILINGS 80 16.3
ALTERNATING SUMS OF TRIANGULAR NUMBERS 80 16.4 IN SPACE, FOUR COLORS ARE
NOT ENOUGH 81 16.5 CHALLENGES 81 17 VISUALIZATION BY INCLUSION 83 17.1
THE GENUINE TRIANGLE INEQUALITY 83 17.2 THE MEAN OF THE SQUARES EXCEEDS
THE SQUARE OF THE MEAN 84 17.3 THE ARITHMETIC MEAN-GEOMETRIC MEAN
INEQUALITY FOR THREE NUMBERS 84 17.4 CHALLENGES 86 18 INGENUITY IN 3D 87
18.1 FROM 3D WITH LOVE 87 18.2 FOLDING AND CUTTING PAPER 89 18.3
UNFOLDING POLYHEDRA 94 18.4 CHALLENGES 96 XIV MATH MADE VISUAL 19 USING
3D MODELS 97 19.1 PLATONIC SECRETS 97 19.2 THE RHOMBIC DODECAHEDRON 104
19.3 THE FERMAT POINT AGAIN 105 19.4 CHALLENGES 106 20 COMBINING
TECHNIQUES 109 20.1 HERON S FORMULA 109 20.2 THE QUADRILATERAL LAW ILL
20.3 PTOLEMY S INEQUALITY 112 20.4 ANOTHER MINIMAL PATH 113 20.5 SLICING
CUBES 114 20.6 VERTICES, FACES, AND POLYHEDRA 114 20.7 CHALLENGES 115
PART II: VISUALIZATION IN THE CLASSROOM 117 MATHEMATICAL DRAWINGS: A
SHORT HISTORICAL PERSPECTIVE 119 ON VISUAL THINKING 121 VISUALIZATION IN
THE CLASSROOM 123 ON THE ROLE OF HANDS-ON MATERIALS 124 EVERYDAY LIFE
OBJECTS AS RESOURCES 127 MAKING MODELS OF POLYHEDRA 133 USING SOAP
BUBBLES 135 LIGHTING RESULTS 136 MIRROR IMAGES 138 TOWARDS CREATIVITY
140 PART III: HINTS AND SOLUTIONS TO THE CHALLENGES 143 CHAPTER 1 145
CHAPTER 2 146 CHAPTER 3 147 CHAPTER 4 148 CHAPTER 5 149 CHAPTER 6 150
CHAPTER 7 150 CHAPTER 8 151 CHAPTER 9 152 CHAPTER 10 153 CHAPTER 11 154
CHAPTER 12 154 CHAPTER 13 155 CHAPTER 14 156 CHAPTER 15 156 CHAPTER 16
157 CHAPTER 17 158 CONTENTS XV CHAPTER 18 159 CHAPTER 19 159 CHAPTER 20
160 REFERENCES 161 INDEX 169 ABOUT THE AUTHORS 173
|
| adam_txt |
MATH MADE VISUAL CREATING IMAGES FOR UNDERSTANDING MATHEMATICS CLAUDI
ALSINA UNIVERSITAT POLITECNICA DE CATALUNYA AND ROGER B. NELSEN LEWIS &
CLARK COLLEGE PUBLISHED AND DISTRIBUTED BY THE MATHEMATICAL ASSOCIATION
OF AMERICA CONTENTS INTRODUCTION IX PART I: VISUALIZING MATHEMATICS BY
CREATING PICTURES 1 1 REPRESENTING NUMBERS BY GRAPHICAL ELEMENTS 3 1 .1
SUMS OF ODD INTEGERS 3 1.2 SUMS OF INTEGERS 4 1.3 ALTERNATING SUMS OF
SQUARES 5 1.4 CHALLENGES 6 2 REPRESENTING NUMBERS BY LENGTHS OF SEGMENTS
7 2.1 INEQUALITIES AMONG MEANS 7 2.2 THE MEDIANT PROPERTY 9 2.3 A
PYTHAGOREAN INEQUALITY 10 2.4 TRIGONOMETRIC FUNCTIONS 10 2.5 NUMBERS AS
FUNCTION VALUES 11 2.6 CHALLENGES 12 3 REPRESENTING NUMBERS BY AREAS OF
PLANE FIGURES 13 3.1 SUMS OF INTEGERS REVISITED 13 3.2 THE SUM OF TERMS
IN ARITHMETIC PROGRESSION 14 3.3 FIBONACCI NUMBERS 15 3.4 SOME
INEQUALITIES 15 3.5 SUMS OF SQUARES 17 3.6 SUMS OF CUBES 17 3.7
CHALLENGES 18 4 REPRESENTING NUMBERS BY VOLUMES OF OBJECTS 19 4.1 FROM
TWO DIMENSIONS TO THREE 19 4.2 SUMS OF SQUARES OF INTEGERS REVISITED 20
4.3 SUMS OF TRIANGULAR NUMBERS 21 4.4 A DOUBLE SUM 21 4.5 CHALLENGES 22
XI XII MATH MADE VISUAL 5 IDENTIFYING KEY ELEMENTS 23 5.1 ON THE ANGLE
BISECTORS OF A CONVEX QUADRILATERAL 23 5.2 CYCLIC QUADRILATERALS WITH
PERPENDICULAR DIAGONALS 24 5.3 A PROPERTY OF THE RECTANGULAR HYPERBOLA
25 5.4 CHALLENGES 25 6 EMPLOYING ISOMETRY 27 6.1 THE CHOU PEI SUAN CHING
PROOF OF THE PYTHAGOREAN THEOREM 27 6.2 A THEOREM OF THALES 27 6.3
LEONARDO DA VINCI'S PROOF OF THE PYTHAGOREAN THEOREM 28 6.4 THE FERMAT
POINT OF A TRIANGLE 29 6.5 VIVIANI'S THEOREM 29 6.6 CHALLENGES 30 7
EMPLOYING SIMILARITY 31 7.1 PTOLEMY'S THEOREM 31 7.2 THE GOLDEN RATIO IN
THE REGULAR PENTAGON 32 7.3 THE PYTHAGOREAN THEOREM*AGAIN 33 7.4 AREA
BETWEEN SIDES AND CEVIANS OF A TRIANGLE 33 7.5 CHALLENGES 34 8
AREA-PRESERVING TRANSFORMATIONS 35 8.1 PAPPUS AND PYTHAGORAS 35 8.2
SQUARING POLYGONS 37 8.3 EQUAL AREAS IN A PARTITION OF A PARALLELOGRAM
38 8.4 THE CAUCHY-SCHWARZ INEQUALITY 38 8.5 A THEOREM OF GASPARD MONGE
39 8.6 CHALLENGES 40 9 ESCAPING FROM THE PLANE 43 9.1 THREE CIRCLES AND
SIX TANGENTS 43 9.2 FAIR DIVISION OF A CAKE 44 9.3 INSCRIBING THE
REGULAR HEPTAGON IN A CIRCLE 44 9.4 THE SPIDER AND THE FLY 45 9.5
CHALLENGES 46 10 OVERLAYING TILES 47 10.1 PYTHAGOREAN TILINGS 47 10.2
CARTESIAN TILINGS 49 10.3 QUADRILATERAL TILINGS 50 10.4 TRIANGULAR
TILINGS 51 10.5 TILING WITH SQUARES AND PARALLELOGRAMS 51 10.6
CHALLENGES 52 11 PLAYING WITH SEVERAL COPIES 55 11.1 FROM PYTHAGORAS TO
TRIGONOMETRY 55 11.2 SUMS OF ODD INTEGERS REVISITED 56 CONTENTS XIII
11.3 SUMS OF SQUARES AGAIN 56 11.4 THE VOLUME OF A SQUARE PYRAMID 57
11.5 CHALLENGES 57 12 SEQUENTIAL FRAMES 59 12.1 THE PARALLELOGRAM LAW 59
12.2 AN UNKNOWN ANGLE 61 12.3 DETERMINANTS 61 12.4 CHALLENGES 62 13
GEOMETRIC DISSECTIONS 63 13.1 CUTTING WITH INGENUITY 64 13.2 THE "SMART
ALEC" PUZZLE 65 13.3 THE AREA OF A REGULAR DODECAGON 66 13.4 CHALLENGES
66 14 MOVING FRAMES 69 14.1 FUNCTIONAL COMPOSITION 69 14.2 THE LIPSCHITZ
CONDITION 70 14.3 UNIFORM CONTINUITY 71 14.4 CHALLENGES 72 15 ITERATIVE
PROCEDURES 73 15.1 GEOMETRIC SERIES 73 15.2 GROWING A FIGURE ITERATIVELY
74 15.3 A CURVE WITHOUT TANGENTS 76 15.4 CHALLENGES 76 16 INTRODUCING
COLORS 79 16.1 DOMINO TILINGS 79 16.2 L-TETROMINO TILINGS 80 16.3
ALTERNATING SUMS OF TRIANGULAR NUMBERS 80 16.4 IN SPACE, FOUR COLORS ARE
NOT ENOUGH 81 16.5 CHALLENGES 81 17 VISUALIZATION BY INCLUSION 83 17.1
THE GENUINE TRIANGLE INEQUALITY 83 17.2 THE MEAN OF THE SQUARES EXCEEDS
THE SQUARE OF THE MEAN 84 17.3 THE ARITHMETIC MEAN-GEOMETRIC MEAN
INEQUALITY FOR THREE NUMBERS 84 17.4 CHALLENGES 86 18 INGENUITY IN 3D 87
18.1 FROM 3D WITH LOVE 87 18.2 FOLDING AND CUTTING PAPER 89 18.3
UNFOLDING POLYHEDRA 94 18.4 CHALLENGES 96 XIV MATH MADE VISUAL 19 USING
3D MODELS 97 19.1 PLATONIC SECRETS 97 19.2 THE RHOMBIC DODECAHEDRON 104
19.3 THE FERMAT POINT AGAIN 105 19.4 CHALLENGES 106 20 COMBINING
TECHNIQUES 109 20.1 HERON'S FORMULA 109 20.2 THE QUADRILATERAL LAW ILL
20.3 PTOLEMY'S INEQUALITY 112 20.4 ANOTHER MINIMAL PATH 113 20.5 SLICING
CUBES 114 20.6 VERTICES, FACES, AND POLYHEDRA 114 20.7 CHALLENGES 115
PART II: VISUALIZATION IN THE CLASSROOM 117 MATHEMATICAL DRAWINGS: A
SHORT HISTORICAL PERSPECTIVE 119 ON VISUAL THINKING 121 VISUALIZATION IN
THE CLASSROOM 123 ON THE ROLE OF HANDS-ON MATERIALS 124 EVERYDAY LIFE
OBJECTS AS RESOURCES 127 MAKING MODELS OF POLYHEDRA 133 USING SOAP
BUBBLES 135 LIGHTING RESULTS 136 MIRROR IMAGES 138 TOWARDS CREATIVITY
140 PART III: HINTS AND SOLUTIONS TO THE CHALLENGES 143 CHAPTER 1 145
CHAPTER 2 146 CHAPTER 3 147 CHAPTER 4 148 CHAPTER 5 149 CHAPTER 6 150
CHAPTER 7 150 CHAPTER 8 151 CHAPTER 9 152 CHAPTER 10 153 CHAPTER 11 154
CHAPTER 12 154 CHAPTER 13 155 CHAPTER 14 156 CHAPTER 15 156 CHAPTER 16
157 CHAPTER 17 158 CONTENTS XV CHAPTER 18 159 CHAPTER 19 159 CHAPTER 20
160 REFERENCES 161 INDEX 169 ABOUT THE AUTHORS 173 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T22:01:44Z |
| indexdate | 2024-07-09T21:21:23Z |
| institution | BVB |
| isbn | 9780883857465 0883857464 |
| language | English |
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| spelling | Alsina, Claudi 1952- Verfasser (DE-588)143990934 aut Math made visual creating images for understanding mathematics Claudi Alsina and Roger B. Nelsen Washington, DC <<The>> Mathematical Assoc. of America 2006 XV, 173 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Classroom resource materials Mathematik Mathematics Study and teaching Mathematics Charts, diagrams, etc Digital images Visualisierung (DE-588)4188417-6 gnd rswk-swf Mathematikunterricht (DE-588)4037949-8 gnd rswk-swf Visualisierung (DE-588)4188417-6 s Mathematikunterricht (DE-588)4037949-8 s DE-604 Nelsen, Roger B. 1942- Verfasser (DE-588)12076945X aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016732922&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Alsina, Claudi 1952- Nelsen, Roger B. 1942- Math made visual creating images for understanding mathematics Mathematik Mathematics Study and teaching Mathematics Charts, diagrams, etc Digital images Visualisierung (DE-588)4188417-6 gnd Mathematikunterricht (DE-588)4037949-8 gnd |
| subject_GND | (DE-588)4188417-6 (DE-588)4037949-8 |
| title | Math made visual creating images for understanding mathematics |
| title_auth | Math made visual creating images for understanding mathematics |
| title_exact_search | Math made visual creating images for understanding mathematics |
| title_exact_search_txtP | Math made visual creating images for understanding mathematics |
| title_full | Math made visual creating images for understanding mathematics Claudi Alsina and Roger B. Nelsen |
| title_fullStr | Math made visual creating images for understanding mathematics Claudi Alsina and Roger B. Nelsen |
| title_full_unstemmed | Math made visual creating images for understanding mathematics Claudi Alsina and Roger B. Nelsen |
| title_short | Math made visual |
| title_sort | math made visual creating images for understanding mathematics |
| title_sub | creating images for understanding mathematics |
| topic | Mathematik Mathematics Study and teaching Mathematics Charts, diagrams, etc Digital images Visualisierung (DE-588)4188417-6 gnd Mathematikunterricht (DE-588)4037949-8 gnd |
| topic_facet | Mathematik Mathematics Study and teaching Mathematics Charts, diagrams, etc Digital images Visualisierung Mathematikunterricht |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016732922&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT alsinaclaudi mathmadevisualcreatingimagesforunderstandingmathematics AT nelsenrogerb mathmadevisualcreatingimagesforunderstandingmathematics |