Math made visual :: creating images for understanding mathematics /
The object of this book is to show how visualization techniques may be employed to produce pictures that have interest for the creation, communication, and teaching of mathematics.
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Washington, DC :
Mathematical Association of America,
©2006.
|
| Schriftenreihe: | Classroom resource materials.
|
| Schlagworte: | |
| Online-Zugang: | DE-862 DE-863 |
| Zusammenfassung: | The object of this book is to show how visualization techniques may be employed to produce pictures that have interest for the creation, communication, and teaching of mathematics. |
| Beschreibung: | 1 online resource (xv, 173 pages) : illustrations |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9781614441007 1614441006 |
Internformat
MARC
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| 100 | 1 | |a Alsina, Claudi, |e author. |0 http://id.loc.gov/authorities/names/n79030525 | |
| 245 | 1 | 0 | |a Math made visual : |b creating images for understanding mathematics / |c Claudi Alsina and Roger B. Nelsen. |
| 260 | |a Washington, DC : |b Mathematical Association of America, |c ©2006. | ||
| 300 | |a 1 online resource (xv, 173 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Classroom resource materials | |
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | 0 | |t Introduction -- |g pt. 1. |t Visualizing mathematics by creating pictures -- |g 1. |t Representing numbers by graphical elements -- |g 1.1. |t Sums of odd integers -- |g 1.2. |t Sums of integers -- |g 1.3. |t Alternating sums of squares -- |g 1.4. |t Challenges -- |g 2. |t Representing numbers by lengths of segments -- |g 2.1. |t Inequalities among means -- |g 2.2. |t The mediant property -- |g 2.3. |t A Pythagorean inequality -- |g 2.4. |t Trigonometric functions -- |g 2.5. |t Numbers as function values -- |g 2.6. |t Challenges -- |g 3. |t Representing numbers by areas of plane figures -- |g 3.1. |t Sums of integers revisited -- |g 3.2. |t The sum of terms in arithmetic progression -- |g 3.3. |t Fibonacci numbers -- |g 3.4. |t Some inequalities -- |g 3.4. |t Some inequalities -- |g 3.5. |t Sums of squares -- |g 3.6. |t Sums of cubes -- |g 3.7. |t Challenges -- |g 4. |t Representing numbers by volumes of objects -- |g 4.1. |t From two dimensions to three -- |g 4.2. |t Sums of squares of integers revisited -- |g 4.3. |t Sums of triangular numbers -- |g 4.4. |t A double sum -- |g 4.5. |t Challenges. |
| 505 | 0 | 0 | |g 5. |t Identifying key elements -- |g 5.1. |t On the angle bisectors of a convex quadrilateral -- |g 5.2. |t Cyclic quadrilaterals with perpendicular diagonals -- |g 5.3. |t A property of the rectangular hyperbola -- |g 5.4. |t Challenges -- |g 6. |t Employing isometry -- |g 6.1. |t The Chou Pei Suan Ching proof of the Pythagorean theorem -- |g 6.2. |t A theorem of Thales -- |g 6.3. |t Leonardo da Vinci's proof of the Pythagorean theorem -- |g 6.4. |t The Fermat point of a triangle -- |g 6.5. |t Viviani's theorem -- |g 6.6. |t Challenges -- |g 7. |t Employing similarity -- |g 7.1. |t Ptolemy's theorem -- |g 7.2. |t The golden ratio in the regular pentagon -- |g 7.3. |t The Pythagorean theorem -- again -- |g 7.4. |t Area between sides and cevians of a triangle -- |g 7.5. |t Challenges -- |g 8. |t Area-preserving transformations -- |g 8.1. |t Pappus and Pythagoras -- |g 8.2. |t Squaring polygons -- |g 8.3. |t Equal areas in a partition of a parallelogram -- |g 8.4. |t The Cauchy-Schwarz inequality -- |g 8.5. |t A theorem of Gaspard Monge -- |g 8.6. |t Challenges. |
| 505 | 0 | 0 | |g 9. |t Escaping from the plane -- |g 9.1. |t Three circles and six tangents -- |g 9.2. |t FAir division of a cake -- |g 9.3. |t Inscribing the regular heptagon in a circle -- |g 9.4. |t The spider and the fly -- |g 9.5. |t Challenges -- |g 10. |t Overlaying tiles -- |g 10.1. |t Pythagorean tilings -- |g 10.2. |t Cartesian tilings -- |g 10.3. |t Quadrilateral tilings -- |g 10.4. |t Triangular tilings -- |g 10.5. |t Tiling with squares and parallelograms -- |g 10.6. |t Challenges -- |g 11. |t Playing with several copies -- |g 11.1. |t From Pythagoras to trigonometry -- |g 11.2. |t Sums of odd integers revisited -- |g 11.3 |t Sums of squares again -- |g 11.4. |t The volume of a square pyramid -- |g 11.5. |t Challenges -- |g 12. |t Sequential frames -- |g 12.1. |t The parallelogram law -- |g 12.2. |t An unknown angle -- |g 12.3. |t Determinants -- |g 12.4. |t Challenges -- |g 13. |t Geometric dissections -- |g 13.1. |t Cutting with ingenuity -- |g 13.2. |t The "smart Alec" puzzle -- |g 13.3. |t The area of a regular dodecagon -- |g 13.4. |t Challenges -- |g 14. |t Moving frames -- |g 14.1. |t Functional composition -- |g 14.2. |t The Lipschitz condition -- |g 14.3. |t Uniform continuity -- |g 14.4. |t Challenges. |
| 505 | 0 | 0 | |g 15. |t Iterative procedures -- |g 15.1. |t Geometric series -- |g 15.2. |t Growing a figure iteratively -- |g 15.3. |t A curve without tangents -- |g 15.4. |t Challenges -- |g 16. |t Introducing colors -- |g 16.1. |t Domino tilings -- |g 16.2. |t L-Tetromino tilings -- |g 16.3. |t Alternating sums of triangular numbers -- |g 16.4. |t In space, four colors are not enough -- |g 16.5. |t Challenges -- |g 17. |t Visualization by inclusion -- |g 17.1. |t The genuine triangle inequality -- |g 17.2. |t The mean of the squares exceeds the square of the mean -- |g 17.3. |t The arithmetic mean-geometric mean inequality for three numbers -- |g 17.4. |t Challenges -- |g 18. |t Ingenuity in 3 D -- |g 18.1. |t From 3D with love -- |g 18.2. |t Folding and cutting paper -- |g 18.3. |t Unfolding polyhedra -- |g 18.4. |t Challenges -- |g 19. |t Using 3D models -- |g 19.1. |t Platonic secrets -- |g 19.2. |t The rhombic dodecahedron -- |g 19.3. |t The Fermat point again -- |g 19.4. |t Challenges -- |g 20. |t Combining techniques -- |g 20.1. |t Heron's formula -- |g 20.2. |t The quadrilateral law -- |g 20.3. |t Ptolemy's inequality -- |g 20.4. |t Another minimal path -- |g 20.5. |t Slicing cubes -- |g 20.6. |t Vertices, faces, and polyhedra -- |g 20.7. |t challenges. |
| 505 | 0 | 0 | |g pt. 2. |t Visualization in the classroom -- |t Mathematical drawings : a short historical perspective -- |t On visual thinking -- |t Visualization in the classroom -- |t On the role of hands-on materials -- |t Everyday life objects as resources -- |t Making models of polyhedra -- |t Using soap bubbles -- |t Lighting results -- |t Mirror images -- |t Towards creativity -- |g pt. 3. |t Hints and solutions to the challenges -- |t References -- |t Index -- |t About the authors. |
| 520 | |a The object of this book is to show how visualization techniques may be employed to produce pictures that have interest for the creation, communication, and teaching of mathematics. | ||
| 588 | 0 | |a Print version record. | |
| 650 | 0 | |a Mathematics |x Study and teaching (Higher) | |
| 650 | 0 | |a Mathematics |v Charts, diagrams, etc. |0 http://id.loc.gov/authorities/subjects/sh85082143 | |
| 650 | 0 | |a Digital images. |0 http://id.loc.gov/authorities/subjects/sh2006002712 | |
| 650 | 6 | |a Images numériques. | |
| 650 | 7 | |a digital images. |2 aat | |
| 650 | 7 | |a MATHEMATICS |x Study & Teaching. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x General. |2 bisacsh | |
| 650 | 7 | |a Digital images |2 fast | |
| 650 | 7 | |a Mathematics |2 fast | |
| 650 | 7 | |a Mathematics |x Study and teaching (Higher) |2 fast | |
| 650 | 7 | |a Mathematikunterricht |2 gnd | |
| 650 | 7 | |a Visualisierung |2 gnd | |
| 655 | 7 | |a Charts, diagrams, etc. |2 fast | |
| 700 | 1 | |a Nelsen, Roger B., |e author. |0 http://id.loc.gov/authorities/names/n94115896 | |
| 758 | |i has work: |a Math made visual (Text) |1 https://id.oclc.org/worldcat/entity/E39PCG6P7DmCcqPgGGxmHDkFcd |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Alsina, Claudi. |t Math made visual. |d Washington, DC : Mathematical Association of America, ©2006 |z 0883857464 |w (DLC) 2005937269 |w (OCoLC)69137417 |
| 830 | 0 | |a Classroom resource materials. | |
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Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn794855553 |
|---|---|
| _version_ | 1829094728348467200 |
| adam_text | |
| any_adam_object | |
| author | Alsina, Claudi Nelsen, Roger B. |
| author_GND | http://id.loc.gov/authorities/names/n79030525 http://id.loc.gov/authorities/names/n94115896 |
| author_facet | Alsina, Claudi Nelsen, Roger B. |
| author_role | aut aut |
| author_sort | Alsina, Claudi |
| author_variant | c a ca r b n rb rbn |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA19 |
| callnumber-raw | QA19.C45 A47 2006 |
| callnumber-search | QA19.C45 A47 2006 |
| callnumber-sort | QA 219 C45 A47 42006 |
| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| contents | Introduction -- Visualizing mathematics by creating pictures -- Representing numbers by graphical elements -- Sums of odd integers -- Sums of integers -- Alternating sums of squares -- Challenges -- Representing numbers by lengths of segments -- Inequalities among means -- The mediant property -- A Pythagorean inequality -- Trigonometric functions -- Numbers as function values -- Representing numbers by areas of plane figures -- Sums of integers revisited -- The sum of terms in arithmetic progression -- Fibonacci numbers -- Some inequalities -- Sums of squares -- Sums of cubes -- Representing numbers by volumes of objects -- From two dimensions to three -- Sums of squares of integers revisited -- Sums of triangular numbers -- A double sum -- Challenges. Identifying key elements -- On the angle bisectors of a convex quadrilateral -- Cyclic quadrilaterals with perpendicular diagonals -- A property of the rectangular hyperbola -- Employing isometry -- The Chou Pei Suan Ching proof of the Pythagorean theorem -- A theorem of Thales -- Leonardo da Vinci's proof of the Pythagorean theorem -- The Fermat point of a triangle -- Viviani's theorem -- Employing similarity -- Ptolemy's theorem -- The golden ratio in the regular pentagon -- The Pythagorean theorem -- again -- Area between sides and cevians of a triangle -- Area-preserving transformations -- Pappus and Pythagoras -- Squaring polygons -- Equal areas in a partition of a parallelogram -- The Cauchy-Schwarz inequality -- A theorem of Gaspard Monge -- Escaping from the plane -- Three circles and six tangents -- FAir division of a cake -- Inscribing the regular heptagon in a circle -- The spider and the fly -- Overlaying tiles -- Pythagorean tilings -- Cartesian tilings -- Quadrilateral tilings -- Triangular tilings -- Tiling with squares and parallelograms -- Playing with several copies -- From Pythagoras to trigonometry -- Sums of odd integers revisited -- Sums of squares again -- The volume of a square pyramid -- Sequential frames -- The parallelogram law -- An unknown angle -- Determinants -- Geometric dissections -- Cutting with ingenuity -- The "smart Alec" puzzle -- The area of a regular dodecagon -- Moving frames -- Functional composition -- The Lipschitz condition -- Uniform continuity -- Iterative procedures -- Geometric series -- Growing a figure iteratively -- A curve without tangents -- Introducing colors -- Domino tilings -- L-Tetromino tilings -- Alternating sums of triangular numbers -- In space, four colors are not enough -- Visualization by inclusion -- The genuine triangle inequality -- The mean of the squares exceeds the square of the mean -- The arithmetic mean-geometric mean inequality for three numbers -- Ingenuity in 3 D -- From 3D with love -- Folding and cutting paper -- Unfolding polyhedra -- Using 3D models -- Platonic secrets -- The rhombic dodecahedron -- The Fermat point again -- Combining techniques -- Heron's formula -- The quadrilateral law -- Ptolemy's inequality -- Another minimal path -- Slicing cubes -- Vertices, faces, and polyhedra -- challenges. Visualization in the classroom -- Mathematical drawings : a short historical perspective -- On visual thinking -- On the role of hands-on materials -- Everyday life objects as resources -- Making models of polyhedra -- Using soap bubbles -- Lighting results -- Mirror images -- Towards creativity -- Hints and solutions to the challenges -- References -- Index -- About the authors. |
| ctrlnum | (OCoLC)794855553 |
| dewey-full | 510.71 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510.71 |
| dewey-search | 510.71 |
| dewey-sort | 3510.71 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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the angle bisectors of a convex quadrilateral --</subfield><subfield code="g">5.2.</subfield><subfield code="t">Cyclic quadrilaterals with perpendicular diagonals --</subfield><subfield code="g">5.3.</subfield><subfield code="t">A property of the rectangular hyperbola --</subfield><subfield code="g">5.4.</subfield><subfield code="t">Challenges --</subfield><subfield code="g">6.</subfield><subfield code="t">Employing isometry --</subfield><subfield code="g">6.1.</subfield><subfield code="t">The Chou Pei Suan Ching proof of the Pythagorean theorem --</subfield><subfield code="g">6.2.</subfield><subfield code="t">A theorem of Thales --</subfield><subfield code="g">6.3.</subfield><subfield code="t">Leonardo da Vinci's proof of the Pythagorean theorem --</subfield><subfield code="g">6.4.</subfield><subfield code="t">The Fermat point of a triangle --</subfield><subfield code="g">6.5.</subfield><subfield code="t">Viviani's theorem --</subfield><subfield code="g">6.6.</subfield><subfield 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code="g">8.4.</subfield><subfield code="t">The Cauchy-Schwarz inequality --</subfield><subfield code="g">8.5.</subfield><subfield code="t">A theorem of Gaspard Monge --</subfield><subfield code="g">8.6.</subfield><subfield code="t">Challenges.</subfield></datafield><datafield tag="505" ind1="0" ind2="0"><subfield code="g">9.</subfield><subfield code="t">Escaping from the plane --</subfield><subfield code="g">9.1.</subfield><subfield code="t">Three circles and six tangents --</subfield><subfield code="g">9.2.</subfield><subfield code="t">FAir division of a cake --</subfield><subfield code="g">9.3.</subfield><subfield code="t">Inscribing the regular heptagon in a circle --</subfield><subfield code="g">9.4.</subfield><subfield code="t">The spider and the fly --</subfield><subfield code="g">9.5.</subfield><subfield code="t">Challenges --</subfield><subfield code="g">10.</subfield><subfield code="t">Overlaying tiles --</subfield><subfield code="g">10.1.</subfield><subfield code="t">Pythagorean tilings --</subfield><subfield code="g">10.2.</subfield><subfield code="t">Cartesian tilings --</subfield><subfield code="g">10.3.</subfield><subfield code="t">Quadrilateral tilings --</subfield><subfield code="g">10.4.</subfield><subfield code="t">Triangular tilings --</subfield><subfield code="g">10.5.</subfield><subfield code="t">Tiling with squares and parallelograms --</subfield><subfield code="g">10.6.</subfield><subfield code="t">Challenges --</subfield><subfield code="g">11.</subfield><subfield code="t">Playing with several copies --</subfield><subfield code="g">11.1.</subfield><subfield code="t">From Pythagoras to trigonometry --</subfield><subfield code="g">11.2.</subfield><subfield code="t">Sums of odd integers revisited --</subfield><subfield code="g">11.3</subfield><subfield code="t">Sums of squares again --</subfield><subfield code="g">11.4.</subfield><subfield code="t">The volume of a square pyramid --</subfield><subfield code="g">11.5.</subfield><subfield code="t">Challenges --</subfield><subfield code="g">12.</subfield><subfield code="t">Sequential frames --</subfield><subfield code="g">12.1.</subfield><subfield code="t">The parallelogram law --</subfield><subfield code="g">12.2.</subfield><subfield code="t">An unknown angle --</subfield><subfield code="g">12.3.</subfield><subfield code="t">Determinants --</subfield><subfield code="g">12.4.</subfield><subfield code="t">Challenges --</subfield><subfield code="g">13.</subfield><subfield code="t">Geometric dissections --</subfield><subfield code="g">13.1.</subfield><subfield code="t">Cutting with ingenuity --</subfield><subfield code="g">13.2.</subfield><subfield code="t">The "smart Alec" puzzle --</subfield><subfield code="g">13.3.</subfield><subfield code="t">The area of a regular dodecagon --</subfield><subfield code="g">13.4.</subfield><subfield code="t">Challenges --</subfield><subfield code="g">14.</subfield><subfield code="t">Moving frames --</subfield><subfield code="g">14.1.</subfield><subfield code="t">Functional composition --</subfield><subfield code="g">14.2.</subfield><subfield code="t">The Lipschitz condition --</subfield><subfield code="g">14.3.</subfield><subfield code="t">Uniform continuity --</subfield><subfield code="g">14.4.</subfield><subfield code="t">Challenges.</subfield></datafield><datafield tag="505" ind1="0" ind2="0"><subfield code="g">15.</subfield><subfield code="t">Iterative procedures --</subfield><subfield code="g">15.1.</subfield><subfield code="t">Geometric series --</subfield><subfield code="g">15.2.</subfield><subfield code="t">Growing a figure iteratively --</subfield><subfield code="g">15.3.</subfield><subfield code="t">A curve without tangents --</subfield><subfield code="g">15.4.</subfield><subfield code="t">Challenges --</subfield><subfield code="g">16.</subfield><subfield code="t">Introducing colors --</subfield><subfield code="g">16.1.</subfield><subfield code="t">Domino tilings --</subfield><subfield code="g">16.2.</subfield><subfield code="t">L-Tetromino tilings --</subfield><subfield code="g">16.3.</subfield><subfield code="t">Alternating sums of triangular numbers --</subfield><subfield code="g">16.4.</subfield><subfield code="t">In space, four colors are not enough --</subfield><subfield code="g">16.5.</subfield><subfield code="t">Challenges --</subfield><subfield code="g">17.</subfield><subfield code="t">Visualization by inclusion --</subfield><subfield code="g">17.1.</subfield><subfield code="t">The genuine triangle inequality --</subfield><subfield code="g">17.2.</subfield><subfield code="t">The mean of the squares exceeds the square of the mean --</subfield><subfield code="g">17.3.</subfield><subfield code="t">The arithmetic mean-geometric mean inequality for three numbers --</subfield><subfield code="g">17.4.</subfield><subfield code="t">Challenges --</subfield><subfield code="g">18.</subfield><subfield code="t">Ingenuity in 3 D --</subfield><subfield code="g">18.1.</subfield><subfield code="t">From 3D with love --</subfield><subfield code="g">18.2.</subfield><subfield code="t">Folding and cutting paper --</subfield><subfield code="g">18.3.</subfield><subfield code="t">Unfolding polyhedra --</subfield><subfield code="g">18.4.</subfield><subfield code="t">Challenges --</subfield><subfield code="g">19.</subfield><subfield code="t">Using 3D models --</subfield><subfield code="g">19.1.</subfield><subfield code="t">Platonic secrets --</subfield><subfield code="g">19.2.</subfield><subfield code="t">The rhombic dodecahedron --</subfield><subfield code="g">19.3.</subfield><subfield code="t">The Fermat point again --</subfield><subfield code="g">19.4.</subfield><subfield code="t">Challenges --</subfield><subfield code="g">20.</subfield><subfield code="t">Combining techniques --</subfield><subfield code="g">20.1.</subfield><subfield code="t">Heron's formula --</subfield><subfield code="g">20.2.</subfield><subfield code="t">The quadrilateral law --</subfield><subfield code="g">20.3.</subfield><subfield code="t">Ptolemy's inequality --</subfield><subfield code="g">20.4.</subfield><subfield code="t">Another minimal path --</subfield><subfield code="g">20.5.</subfield><subfield code="t">Slicing cubes --</subfield><subfield code="g">20.6.</subfield><subfield code="t">Vertices, faces, and polyhedra --</subfield><subfield code="g">20.7.</subfield><subfield code="t">challenges.</subfield></datafield><datafield tag="505" ind1="0" ind2="0"><subfield code="g">pt. 2.</subfield><subfield code="t">Visualization in the classroom --</subfield><subfield code="t">Mathematical drawings : a short historical perspective --</subfield><subfield code="t">On visual thinking --</subfield><subfield code="t">Visualization in the classroom --</subfield><subfield code="t">On the role of hands-on materials --</subfield><subfield code="t">Everyday life objects as resources --</subfield><subfield code="t">Making models of polyhedra --</subfield><subfield code="t">Using soap bubbles --</subfield><subfield code="t">Lighting results --</subfield><subfield code="t">Mirror images --</subfield><subfield code="t">Towards creativity --</subfield><subfield code="g">pt. 3.</subfield><subfield code="t">Hints and solutions to the challenges --</subfield><subfield code="t">References --</subfield><subfield code="t">Index --</subfield><subfield code="t">About the authors.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">The object of this book is to show how visualization techniques may be employed to produce pictures that have interest for the creation, communication, and teaching of mathematics.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Mathematics</subfield><subfield code="x">Study and teaching (Higher)</subfield></datafield><datafield tag="650" 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| genre | Charts, diagrams, etc. fast |
| genre_facet | Charts, diagrams, etc. |
| id | ZDB-4-EBA-ocn794855553 |
| illustrated | Illustrated |
| indexdate | 2025-04-11T08:37:44Z |
| institution | BVB |
| isbn | 9781614441007 1614441006 |
| language | English |
| lccn | 2005937269 |
| oclc_num | 794855553 |
| open_access_boolean | |
| owner | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
| physical | 1 online resource (xv, 173 pages) : illustrations |
| psigel | ZDB-4-EBA FWS_PDA_EBA ZDB-4-EBA |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Mathematical Association of America, |
| record_format | marc |
| series | Classroom resource materials. |
| series2 | Classroom resource materials |
| spelling | Alsina, Claudi, author. http://id.loc.gov/authorities/names/n79030525 Math made visual : creating images for understanding mathematics / Claudi Alsina and Roger B. Nelsen. Washington, DC : Mathematical Association of America, ©2006. 1 online resource (xv, 173 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Classroom resource materials Includes bibliographical references and index. Introduction -- pt. 1. Visualizing mathematics by creating pictures -- 1. Representing numbers by graphical elements -- 1.1. Sums of odd integers -- 1.2. Sums of integers -- 1.3. Alternating sums of squares -- 1.4. Challenges -- 2. Representing numbers by lengths of segments -- 2.1. Inequalities among means -- 2.2. The mediant property -- 2.3. A Pythagorean inequality -- 2.4. Trigonometric functions -- 2.5. Numbers as function values -- 2.6. Challenges -- 3. Representing numbers by areas of plane figures -- 3.1. Sums of integers revisited -- 3.2. The sum of terms in arithmetic progression -- 3.3. Fibonacci numbers -- 3.4. Some inequalities -- 3.4. Some inequalities -- 3.5. Sums of squares -- 3.6. Sums of cubes -- 3.7. Challenges -- 4. Representing numbers by volumes of objects -- 4.1. From two dimensions to three -- 4.2. Sums of squares of integers revisited -- 4.3. Sums of triangular numbers -- 4.4. A double sum -- 4.5. Challenges. 5. Identifying key elements -- 5.1. On the angle bisectors of a convex quadrilateral -- 5.2. Cyclic quadrilaterals with perpendicular diagonals -- 5.3. A property of the rectangular hyperbola -- 5.4. Challenges -- 6. Employing isometry -- 6.1. The Chou Pei Suan Ching proof of the Pythagorean theorem -- 6.2. A theorem of Thales -- 6.3. Leonardo da Vinci's proof of the Pythagorean theorem -- 6.4. The Fermat point of a triangle -- 6.5. Viviani's theorem -- 6.6. Challenges -- 7. Employing similarity -- 7.1. Ptolemy's theorem -- 7.2. The golden ratio in the regular pentagon -- 7.3. The Pythagorean theorem -- again -- 7.4. Area between sides and cevians of a triangle -- 7.5. Challenges -- 8. Area-preserving transformations -- 8.1. Pappus and Pythagoras -- 8.2. Squaring polygons -- 8.3. Equal areas in a partition of a parallelogram -- 8.4. The Cauchy-Schwarz inequality -- 8.5. A theorem of Gaspard Monge -- 8.6. Challenges. 9. Escaping from the plane -- 9.1. Three circles and six tangents -- 9.2. FAir division of a cake -- 9.3. Inscribing the regular heptagon in a circle -- 9.4. The spider and the fly -- 9.5. Challenges -- 10. Overlaying tiles -- 10.1. Pythagorean tilings -- 10.2. Cartesian tilings -- 10.3. Quadrilateral tilings -- 10.4. Triangular tilings -- 10.5. Tiling with squares and parallelograms -- 10.6. Challenges -- 11. Playing with several copies -- 11.1. From Pythagoras to trigonometry -- 11.2. Sums of odd integers revisited -- 11.3 Sums of squares again -- 11.4. The volume of a square pyramid -- 11.5. Challenges -- 12. Sequential frames -- 12.1. The parallelogram law -- 12.2. An unknown angle -- 12.3. Determinants -- 12.4. Challenges -- 13. Geometric dissections -- 13.1. Cutting with ingenuity -- 13.2. The "smart Alec" puzzle -- 13.3. The area of a regular dodecagon -- 13.4. Challenges -- 14. Moving frames -- 14.1. Functional composition -- 14.2. The Lipschitz condition -- 14.3. Uniform continuity -- 14.4. Challenges. 15. Iterative procedures -- 15.1. Geometric series -- 15.2. Growing a figure iteratively -- 15.3. A curve without tangents -- 15.4. Challenges -- 16. Introducing colors -- 16.1. Domino tilings -- 16.2. L-Tetromino tilings -- 16.3. Alternating sums of triangular numbers -- 16.4. In space, four colors are not enough -- 16.5. Challenges -- 17. Visualization by inclusion -- 17.1. The genuine triangle inequality -- 17.2. The mean of the squares exceeds the square of the mean -- 17.3. The arithmetic mean-geometric mean inequality for three numbers -- 17.4. Challenges -- 18. Ingenuity in 3 D -- 18.1. From 3D with love -- 18.2. Folding and cutting paper -- 18.3. Unfolding polyhedra -- 18.4. Challenges -- 19. Using 3D models -- 19.1. Platonic secrets -- 19.2. The rhombic dodecahedron -- 19.3. The Fermat point again -- 19.4. Challenges -- 20. Combining techniques -- 20.1. Heron's formula -- 20.2. The quadrilateral law -- 20.3. Ptolemy's inequality -- 20.4. Another minimal path -- 20.5. Slicing cubes -- 20.6. Vertices, faces, and polyhedra -- 20.7. challenges. pt. 2. Visualization in the classroom -- Mathematical drawings : a short historical perspective -- On visual thinking -- Visualization in the classroom -- On the role of hands-on materials -- Everyday life objects as resources -- Making models of polyhedra -- Using soap bubbles -- Lighting results -- Mirror images -- Towards creativity -- pt. 3. Hints and solutions to the challenges -- References -- Index -- About the authors. The object of this book is to show how visualization techniques may be employed to produce pictures that have interest for the creation, communication, and teaching of mathematics. Print version record. Mathematics Study and teaching (Higher) Mathematics Charts, diagrams, etc. http://id.loc.gov/authorities/subjects/sh85082143 Digital images. http://id.loc.gov/authorities/subjects/sh2006002712 Images numériques. digital images. aat MATHEMATICS Study & Teaching. bisacsh MATHEMATICS General. bisacsh Digital images fast Mathematics fast Mathematics Study and teaching (Higher) fast Mathematikunterricht gnd Visualisierung gnd Charts, diagrams, etc. fast Nelsen, Roger B., author. http://id.loc.gov/authorities/names/n94115896 has work: Math made visual (Text) https://id.oclc.org/worldcat/entity/E39PCG6P7DmCcqPgGGxmHDkFcd https://id.oclc.org/worldcat/ontology/hasWork Print version: Alsina, Claudi. Math made visual. Washington, DC : Mathematical Association of America, ©2006 0883857464 (DLC) 2005937269 (OCoLC)69137417 Classroom resource materials. |
| spellingShingle | Alsina, Claudi Nelsen, Roger B. Math made visual : creating images for understanding mathematics / Classroom resource materials. Introduction -- Visualizing mathematics by creating pictures -- Representing numbers by graphical elements -- Sums of odd integers -- Sums of integers -- Alternating sums of squares -- Challenges -- Representing numbers by lengths of segments -- Inequalities among means -- The mediant property -- A Pythagorean inequality -- Trigonometric functions -- Numbers as function values -- Representing numbers by areas of plane figures -- Sums of integers revisited -- The sum of terms in arithmetic progression -- Fibonacci numbers -- Some inequalities -- Sums of squares -- Sums of cubes -- Representing numbers by volumes of objects -- From two dimensions to three -- Sums of squares of integers revisited -- Sums of triangular numbers -- A double sum -- Challenges. Identifying key elements -- On the angle bisectors of a convex quadrilateral -- Cyclic quadrilaterals with perpendicular diagonals -- A property of the rectangular hyperbola -- Employing isometry -- The Chou Pei Suan Ching proof of the Pythagorean theorem -- A theorem of Thales -- Leonardo da Vinci's proof of the Pythagorean theorem -- The Fermat point of a triangle -- Viviani's theorem -- Employing similarity -- Ptolemy's theorem -- The golden ratio in the regular pentagon -- The Pythagorean theorem -- again -- Area between sides and cevians of a triangle -- Area-preserving transformations -- Pappus and Pythagoras -- Squaring polygons -- Equal areas in a partition of a parallelogram -- The Cauchy-Schwarz inequality -- A theorem of Gaspard Monge -- Escaping from the plane -- Three circles and six tangents -- FAir division of a cake -- Inscribing the regular heptagon in a circle -- The spider and the fly -- Overlaying tiles -- Pythagorean tilings -- Cartesian tilings -- Quadrilateral tilings -- Triangular tilings -- Tiling with squares and parallelograms -- Playing with several copies -- From Pythagoras to trigonometry -- Sums of odd integers revisited -- Sums of squares again -- The volume of a square pyramid -- Sequential frames -- The parallelogram law -- An unknown angle -- Determinants -- Geometric dissections -- Cutting with ingenuity -- The "smart Alec" puzzle -- The area of a regular dodecagon -- Moving frames -- Functional composition -- The Lipschitz condition -- Uniform continuity -- Iterative procedures -- Geometric series -- Growing a figure iteratively -- A curve without tangents -- Introducing colors -- Domino tilings -- L-Tetromino tilings -- Alternating sums of triangular numbers -- In space, four colors are not enough -- Visualization by inclusion -- The genuine triangle inequality -- The mean of the squares exceeds the square of the mean -- The arithmetic mean-geometric mean inequality for three numbers -- Ingenuity in 3 D -- From 3D with love -- Folding and cutting paper -- Unfolding polyhedra -- Using 3D models -- Platonic secrets -- The rhombic dodecahedron -- The Fermat point again -- Combining techniques -- Heron's formula -- The quadrilateral law -- Ptolemy's inequality -- Another minimal path -- Slicing cubes -- Vertices, faces, and polyhedra -- challenges. Visualization in the classroom -- Mathematical drawings : a short historical perspective -- On visual thinking -- On the role of hands-on materials -- Everyday life objects as resources -- Making models of polyhedra -- Using soap bubbles -- Lighting results -- Mirror images -- Towards creativity -- Hints and solutions to the challenges -- References -- Index -- About the authors. Mathematics Study and teaching (Higher) Mathematics Charts, diagrams, etc. http://id.loc.gov/authorities/subjects/sh85082143 Digital images. http://id.loc.gov/authorities/subjects/sh2006002712 Images numériques. digital images. aat MATHEMATICS Study & Teaching. bisacsh MATHEMATICS General. bisacsh Digital images fast Mathematics fast Mathematics Study and teaching (Higher) fast Mathematikunterricht gnd Visualisierung gnd |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85082143 http://id.loc.gov/authorities/subjects/sh2006002712 |
| title | Math made visual : creating images for understanding mathematics / |
| title_alt | Introduction -- Visualizing mathematics by creating pictures -- Representing numbers by graphical elements -- Sums of odd integers -- Sums of integers -- Alternating sums of squares -- Challenges -- Representing numbers by lengths of segments -- Inequalities among means -- The mediant property -- A Pythagorean inequality -- Trigonometric functions -- Numbers as function values -- Representing numbers by areas of plane figures -- Sums of integers revisited -- The sum of terms in arithmetic progression -- Fibonacci numbers -- Some inequalities -- Sums of squares -- Sums of cubes -- Representing numbers by volumes of objects -- From two dimensions to three -- Sums of squares of integers revisited -- Sums of triangular numbers -- A double sum -- Challenges. Identifying key elements -- On the angle bisectors of a convex quadrilateral -- Cyclic quadrilaterals with perpendicular diagonals -- A property of the rectangular hyperbola -- Employing isometry -- The Chou Pei Suan Ching proof of the Pythagorean theorem -- A theorem of Thales -- Leonardo da Vinci's proof of the Pythagorean theorem -- The Fermat point of a triangle -- Viviani's theorem -- Employing similarity -- Ptolemy's theorem -- The golden ratio in the regular pentagon -- The Pythagorean theorem -- again -- Area between sides and cevians of a triangle -- Area-preserving transformations -- Pappus and Pythagoras -- Squaring polygons -- Equal areas in a partition of a parallelogram -- The Cauchy-Schwarz inequality -- A theorem of Gaspard Monge -- Escaping from the plane -- Three circles and six tangents -- FAir division of a cake -- Inscribing the regular heptagon in a circle -- The spider and the fly -- Overlaying tiles -- Pythagorean tilings -- Cartesian tilings -- Quadrilateral tilings -- Triangular tilings -- Tiling with squares and parallelograms -- Playing with several copies -- From Pythagoras to trigonometry -- Sums of odd integers revisited -- Sums of squares again -- The volume of a square pyramid -- Sequential frames -- The parallelogram law -- An unknown angle -- Determinants -- Geometric dissections -- Cutting with ingenuity -- The "smart Alec" puzzle -- The area of a regular dodecagon -- Moving frames -- Functional composition -- The Lipschitz condition -- Uniform continuity -- Iterative procedures -- Geometric series -- Growing a figure iteratively -- A curve without tangents -- Introducing colors -- Domino tilings -- L-Tetromino tilings -- Alternating sums of triangular numbers -- In space, four colors are not enough -- Visualization by inclusion -- The genuine triangle inequality -- The mean of the squares exceeds the square of the mean -- The arithmetic mean-geometric mean inequality for three numbers -- Ingenuity in 3 D -- From 3D with love -- Folding and cutting paper -- Unfolding polyhedra -- Using 3D models -- Platonic secrets -- The rhombic dodecahedron -- The Fermat point again -- Combining techniques -- Heron's formula -- The quadrilateral law -- Ptolemy's inequality -- Another minimal path -- Slicing cubes -- Vertices, faces, and polyhedra -- challenges. Visualization in the classroom -- Mathematical drawings : a short historical perspective -- On visual thinking -- On the role of hands-on materials -- Everyday life objects as resources -- Making models of polyhedra -- Using soap bubbles -- Lighting results -- Mirror images -- Towards creativity -- Hints and solutions to the challenges -- References -- Index -- About the authors. |
| title_auth | Math made visual : creating images for understanding mathematics / |
| title_exact_search | 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 | Mathematics Study and teaching (Higher) Mathematics Charts, diagrams, etc. http://id.loc.gov/authorities/subjects/sh85082143 Digital images. http://id.loc.gov/authorities/subjects/sh2006002712 Images numériques. digital images. aat MATHEMATICS Study & Teaching. bisacsh MATHEMATICS General. bisacsh Digital images fast Mathematics fast Mathematics Study and teaching (Higher) fast Mathematikunterricht gnd Visualisierung gnd |
| topic_facet | Mathematics Study and teaching (Higher) Mathematics Charts, diagrams, etc. Digital images. Images numériques. digital images. MATHEMATICS Study & Teaching. MATHEMATICS General. Digital images Mathematics Mathematikunterricht Visualisierung Charts, diagrams, etc. |
| work_keys_str_mv | AT alsinaclaudi mathmadevisualcreatingimagesforunderstandingmathematics AT nelsenrogerb mathmadevisualcreatingimagesforunderstandingmathematics |