Origamics :: mathematical explorations through paper folding /
In this unique and original book, origami is an object of mathematical exploration. The activities in this book differ from ordinary origami in that no figures of objects result. Rather, they lead the reader to study the effects of the folding and seek patterns. The experimental approach that charac...
Gespeichert in:
| 1. Verfasser: | |
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| Weitere Verfasser: | , |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore ; Hackensack, N.J. :
World Scientific Pub. Co.,
©2008.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | In this unique and original book, origami is an object of mathematical exploration. The activities in this book differ from ordinary origami in that no figures of objects result. Rather, they lead the reader to study the effects of the folding and seek patterns. The experimental approach that characterizes much of science activity can be recognized throughout the book, as the manipulative nature of origami allows much experimenting, comparing, visualizing, discovering and conjecturing. |
| Beschreibung: | 9. Where to go and whom to meet. 9.1. An origamics activity as a game. 9.2. A scenario: a princess and three knights? 9.3. The rule: one guest at a time. 9.4. Cases where no interview is possible. 9.5. Mapping the neighborhood. 9.6. A flower pattern or an insect pattern. 9.7. A different rule: group meetings. 9.8. Are there areas where a particular male can have exclusive meetings with the female? 9.9. More meetings through a "hidden door." |
| Beschreibung: | 1 online resource |
| ISBN: | 9789812834911 9812834915 |
Internformat
MARC
| LEADER | 00000cam a2200000Ma 4500 | ||
|---|---|---|---|
| 001 | ZDB-4-EBA-ocn820944619 | ||
| 003 | OCoLC | ||
| 005 | 20241004212047.0 | ||
| 006 | m o d | ||
| 007 | cr cn||||||||| | ||
| 008 | 090522s2008 si a o 000 0 eng d | ||
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| 100 | 1 | |a Haga, Kazuo, |d 1934- |1 https://id.oclc.org/worldcat/entity/E39PBJktv9b8F8DhYBvPPXmGHC |0 http://id.loc.gov/authorities/names/no2009050949 | |
| 240 | 1 | 0 | |a Origamikusu. |l English |
| 245 | 1 | 0 | |a Origamics : |b mathematical explorations through paper folding / |c Kazuo Haga ; edited and translated by Josefina C. Fonacier, Masami Isoda. |
| 260 | |a Singapore ; |a Hackensack, N.J. : |b World Scientific Pub. Co., |c ©2008. | ||
| 300 | |a 1 online resource | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
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| 505 | 0 | |a 1. A point opens the door to origamics. 1.1. Simple questions about origami. 1.2. Constructing a pythagorean triangle. 1.3. Dividing a line segment into three equal parts using no tools. 1.4. Extending toward a generalization -- 2. New folds bring out new theorems. 2.1. Trisecting a line segment using Haga's second theorem field. 2.2. The position of point F is interesting. 2.3. Some findings related to Haga's third theorem fold -- 3. Extension of the Haga's theorems to silver ratio rectangles. 3.1. Mathematical adventure by folding a copy paper. 3.2. Mysteries revealed from horizontal folding of copy paper. 3.3. Using standard copy paper with Haga's third theorem. | |
| 505 | 0 | |a 4. X-lines with lots of surprises. 4.1. We begin with an arbitrary point. 4.2. Revelations concerning the points of intersection. 4.3. The center of the circumcircle! 4.4. How does the vertical position of the point of intersection vary? 4.5. Wonders still continue. 4.6. Solving the riddle of "[symbol]". 4.7. Another wonder -- 5. "Intrasquares" and "extrasquares". 5.1. Do not fold exactly into halves. 5.2. What kind of polygons can you get? 5.3. How do you get a triangle or a quadrilateral? 5.4. Now to making a map. 5.5. This is the "scientific method". 5.6. Completing the map. 5.7. We must also make the map of the outer subdivision. 5.8. Let us calculate areas. | |
| 505 | 0 | |a 6. A petal pattern from hexagons. 6.1. The origamics logo. 6.2. Folding a piece of paper by concentrating the four vertices at one point. 6.3. Remarks on polygonal figures of type n. 6.4. An approach to the problem using group study. 6.5. Reducing the work of paper folding; one eighth of the square will do. 6.6. Why does the petal pattern appear? 6.7. What are the areas of the regions? -- 7. Heptagon regions exist? 7.1. Review of the folding procedure. 7.2. A heptagon appears! 7.3. Experimenting with rectangles with different ratios of sides. 7.4. Try a rhombus -- 8. A wonder of eleven stars. 8.1. Experimenting with paper folding. 8.2. Discovering. 8.3. Proof. 8.4. Morer revelations regarding the intersections of the extensions of the creases. 8.5. Proof of the observation on the intersection points of extended edge-to-line creases. 8.6. The joy of discovering and the excitement of further searching. | |
| 500 | |a 9. Where to go and whom to meet. 9.1. An origamics activity as a game. 9.2. A scenario: a princess and three knights? 9.3. The rule: one guest at a time. 9.4. Cases where no interview is possible. 9.5. Mapping the neighborhood. 9.6. A flower pattern or an insect pattern. 9.7. A different rule: group meetings. 9.8. Are there areas where a particular male can have exclusive meetings with the female? 9.9. More meetings through a "hidden door." | ||
| 505 | 0 | |a 10. Inspiration from rectangular paper. 10.1. A scenario: the stern king of Origami Land. 10.2. Begin with a simpler problem: how to divide the rectangle horizontally and vertically into 3 equal parts. 10.3. A 5-parts division point; the pendulum idea helps. 10.4. A method for finding a 7-parts division point. 10.5. The investigation continues: try the pendulum idea on the 7-parts division method. 10.6. The search for 11-parts and 13-parts division point. 10.7. Another method for finding 11-parts and 13-parts division points. 10.8. Continue the trend of thought: 15-parts and 17-parts division points. 10.9. Some ideas related to the ratios for equal-parts division based on similar triangles. 10.10. Towards more division parts. 10.11. Generalizing to all rectangles. | |
| 520 | |a In this unique and original book, origami is an object of mathematical exploration. The activities in this book differ from ordinary origami in that no figures of objects result. Rather, they lead the reader to study the effects of the folding and seek patterns. The experimental approach that characterizes much of science activity can be recognized throughout the book, as the manipulative nature of origami allows much experimenting, comparing, visualizing, discovering and conjecturing. | ||
| 650 | 0 | |a Origami. |0 http://id.loc.gov/authorities/subjects/sh85095643 | |
| 650 | 0 | |a Polyhedra |x Models. |0 http://id.loc.gov/authorities/subjects/sh85104648 | |
| 650 | 6 | |a Origami. | |
| 650 | 6 | |a Polyèdres |x Modèles. | |
| 650 | 7 | |a GAMES |x Sudoku. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Recreations & Games. |2 bisacsh | |
| 650 | 7 | |a Origami |2 fast | |
| 650 | 7 | |a Polyhedra |x Models |2 fast | |
| 700 | 1 | |a Fonacier, Josefina. | |
| 700 | 1 | |a Isoda, Masami. | |
| 758 | |i has work: |a Origamics (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGggCXKYftXXV34Hd8wxTb |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 856 | 4 | 0 | |l FWS01 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=521237 |3 Volltext |
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Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn820944619 |
|---|---|
| _version_ | 1816882216504918018 |
| adam_text | |
| any_adam_object | |
| author | Haga, Kazuo, 1934- |
| author2 | Fonacier, Josefina Isoda, Masami |
| author2_role | |
| author2_variant | j f jf m i mi |
| author_GND | http://id.loc.gov/authorities/names/no2009050949 |
| author_facet | Haga, Kazuo, 1934- Fonacier, Josefina Isoda, Masami |
| author_role | |
| author_sort | Haga, Kazuo, 1934- |
| author_variant | k h kh |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA491 |
| callnumber-raw | QA491 |
| callnumber-search | QA491 |
| callnumber-sort | QA 3491 |
| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| contents | 1. A point opens the door to origamics. 1.1. Simple questions about origami. 1.2. Constructing a pythagorean triangle. 1.3. Dividing a line segment into three equal parts using no tools. 1.4. Extending toward a generalization -- 2. New folds bring out new theorems. 2.1. Trisecting a line segment using Haga's second theorem field. 2.2. The position of point F is interesting. 2.3. Some findings related to Haga's third theorem fold -- 3. Extension of the Haga's theorems to silver ratio rectangles. 3.1. Mathematical adventure by folding a copy paper. 3.2. Mysteries revealed from horizontal folding of copy paper. 3.3. Using standard copy paper with Haga's third theorem. 4. X-lines with lots of surprises. 4.1. We begin with an arbitrary point. 4.2. Revelations concerning the points of intersection. 4.3. The center of the circumcircle! 4.4. How does the vertical position of the point of intersection vary? 4.5. Wonders still continue. 4.6. Solving the riddle of "[symbol]". 4.7. Another wonder -- 5. "Intrasquares" and "extrasquares". 5.1. Do not fold exactly into halves. 5.2. What kind of polygons can you get? 5.3. How do you get a triangle or a quadrilateral? 5.4. Now to making a map. 5.5. This is the "scientific method". 5.6. Completing the map. 5.7. We must also make the map of the outer subdivision. 5.8. Let us calculate areas. 6. A petal pattern from hexagons. 6.1. The origamics logo. 6.2. Folding a piece of paper by concentrating the four vertices at one point. 6.3. Remarks on polygonal figures of type n. 6.4. An approach to the problem using group study. 6.5. Reducing the work of paper folding; one eighth of the square will do. 6.6. Why does the petal pattern appear? 6.7. What are the areas of the regions? -- 7. Heptagon regions exist? 7.1. Review of the folding procedure. 7.2. A heptagon appears! 7.3. Experimenting with rectangles with different ratios of sides. 7.4. Try a rhombus -- 8. A wonder of eleven stars. 8.1. Experimenting with paper folding. 8.2. Discovering. 8.3. Proof. 8.4. Morer revelations regarding the intersections of the extensions of the creases. 8.5. Proof of the observation on the intersection points of extended edge-to-line creases. 8.6. The joy of discovering and the excitement of further searching. 10. Inspiration from rectangular paper. 10.1. A scenario: the stern king of Origami Land. 10.2. Begin with a simpler problem: how to divide the rectangle horizontally and vertically into 3 equal parts. 10.3. A 5-parts division point; the pendulum idea helps. 10.4. A method for finding a 7-parts division point. 10.5. The investigation continues: try the pendulum idea on the 7-parts division method. 10.6. The search for 11-parts and 13-parts division point. 10.7. Another method for finding 11-parts and 13-parts division points. 10.8. Continue the trend of thought: 15-parts and 17-parts division points. 10.9. Some ideas related to the ratios for equal-parts division based on similar triangles. 10.10. Towards more division parts. 10.11. Generalizing to all rectangles. |
| ctrlnum | (OCoLC)820944619 |
| dewey-full | 793.74 |
| dewey-hundreds | 700 - The arts |
| dewey-ones | 793 - Indoor games and amusements |
| dewey-raw | 793.74 |
| dewey-search | 793.74 |
| dewey-sort | 3793.74 |
| dewey-tens | 790 - Recreational and performing arts |
| discipline | Sport |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn820944619 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:25:05Z |
| institution | BVB |
| isbn | 9789812834911 9812834915 |
| language | English |
| oclc_num | 820944619 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource |
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| publisher | World Scientific Pub. Co., |
| record_format | marc |
| spelling | Haga, Kazuo, 1934- https://id.oclc.org/worldcat/entity/E39PBJktv9b8F8DhYBvPPXmGHC http://id.loc.gov/authorities/names/no2009050949 Origamikusu. English Origamics : mathematical explorations through paper folding / Kazuo Haga ; edited and translated by Josefina C. Fonacier, Masami Isoda. Singapore ; Hackensack, N.J. : World Scientific Pub. Co., ©2008. 1 online resource text txt rdacontent computer c rdamedia online resource cr rdacarrier 1. A point opens the door to origamics. 1.1. Simple questions about origami. 1.2. Constructing a pythagorean triangle. 1.3. Dividing a line segment into three equal parts using no tools. 1.4. Extending toward a generalization -- 2. New folds bring out new theorems. 2.1. Trisecting a line segment using Haga's second theorem field. 2.2. The position of point F is interesting. 2.3. Some findings related to Haga's third theorem fold -- 3. Extension of the Haga's theorems to silver ratio rectangles. 3.1. Mathematical adventure by folding a copy paper. 3.2. Mysteries revealed from horizontal folding of copy paper. 3.3. Using standard copy paper with Haga's third theorem. 4. X-lines with lots of surprises. 4.1. We begin with an arbitrary point. 4.2. Revelations concerning the points of intersection. 4.3. The center of the circumcircle! 4.4. How does the vertical position of the point of intersection vary? 4.5. Wonders still continue. 4.6. Solving the riddle of "[symbol]". 4.7. Another wonder -- 5. "Intrasquares" and "extrasquares". 5.1. Do not fold exactly into halves. 5.2. What kind of polygons can you get? 5.3. How do you get a triangle or a quadrilateral? 5.4. Now to making a map. 5.5. This is the "scientific method". 5.6. Completing the map. 5.7. We must also make the map of the outer subdivision. 5.8. Let us calculate areas. 6. A petal pattern from hexagons. 6.1. The origamics logo. 6.2. Folding a piece of paper by concentrating the four vertices at one point. 6.3. Remarks on polygonal figures of type n. 6.4. An approach to the problem using group study. 6.5. Reducing the work of paper folding; one eighth of the square will do. 6.6. Why does the petal pattern appear? 6.7. What are the areas of the regions? -- 7. Heptagon regions exist? 7.1. Review of the folding procedure. 7.2. A heptagon appears! 7.3. Experimenting with rectangles with different ratios of sides. 7.4. Try a rhombus -- 8. A wonder of eleven stars. 8.1. Experimenting with paper folding. 8.2. Discovering. 8.3. Proof. 8.4. Morer revelations regarding the intersections of the extensions of the creases. 8.5. Proof of the observation on the intersection points of extended edge-to-line creases. 8.6. The joy of discovering and the excitement of further searching. 9. Where to go and whom to meet. 9.1. An origamics activity as a game. 9.2. A scenario: a princess and three knights? 9.3. The rule: one guest at a time. 9.4. Cases where no interview is possible. 9.5. Mapping the neighborhood. 9.6. A flower pattern or an insect pattern. 9.7. A different rule: group meetings. 9.8. Are there areas where a particular male can have exclusive meetings with the female? 9.9. More meetings through a "hidden door." 10. Inspiration from rectangular paper. 10.1. A scenario: the stern king of Origami Land. 10.2. Begin with a simpler problem: how to divide the rectangle horizontally and vertically into 3 equal parts. 10.3. A 5-parts division point; the pendulum idea helps. 10.4. A method for finding a 7-parts division point. 10.5. The investigation continues: try the pendulum idea on the 7-parts division method. 10.6. The search for 11-parts and 13-parts division point. 10.7. Another method for finding 11-parts and 13-parts division points. 10.8. Continue the trend of thought: 15-parts and 17-parts division points. 10.9. Some ideas related to the ratios for equal-parts division based on similar triangles. 10.10. Towards more division parts. 10.11. Generalizing to all rectangles. In this unique and original book, origami is an object of mathematical exploration. The activities in this book differ from ordinary origami in that no figures of objects result. Rather, they lead the reader to study the effects of the folding and seek patterns. The experimental approach that characterizes much of science activity can be recognized throughout the book, as the manipulative nature of origami allows much experimenting, comparing, visualizing, discovering and conjecturing. Origami. http://id.loc.gov/authorities/subjects/sh85095643 Polyhedra Models. http://id.loc.gov/authorities/subjects/sh85104648 Origami. Polyèdres Modèles. GAMES Sudoku. bisacsh MATHEMATICS Recreations & Games. bisacsh Origami fast Polyhedra Models fast Fonacier, Josefina. Isoda, Masami. has work: Origamics (Text) https://id.oclc.org/worldcat/entity/E39PCGggCXKYftXXV34Hd8wxTb https://id.oclc.org/worldcat/ontology/hasWork FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=521237 Volltext |
| spellingShingle | Haga, Kazuo, 1934- Origamics : mathematical explorations through paper folding / 1. A point opens the door to origamics. 1.1. Simple questions about origami. 1.2. Constructing a pythagorean triangle. 1.3. Dividing a line segment into three equal parts using no tools. 1.4. Extending toward a generalization -- 2. New folds bring out new theorems. 2.1. Trisecting a line segment using Haga's second theorem field. 2.2. The position of point F is interesting. 2.3. Some findings related to Haga's third theorem fold -- 3. Extension of the Haga's theorems to silver ratio rectangles. 3.1. Mathematical adventure by folding a copy paper. 3.2. Mysteries revealed from horizontal folding of copy paper. 3.3. Using standard copy paper with Haga's third theorem. 4. X-lines with lots of surprises. 4.1. We begin with an arbitrary point. 4.2. Revelations concerning the points of intersection. 4.3. The center of the circumcircle! 4.4. How does the vertical position of the point of intersection vary? 4.5. Wonders still continue. 4.6. Solving the riddle of "[symbol]". 4.7. Another wonder -- 5. "Intrasquares" and "extrasquares". 5.1. Do not fold exactly into halves. 5.2. What kind of polygons can you get? 5.3. How do you get a triangle or a quadrilateral? 5.4. Now to making a map. 5.5. This is the "scientific method". 5.6. Completing the map. 5.7. We must also make the map of the outer subdivision. 5.8. Let us calculate areas. 6. A petal pattern from hexagons. 6.1. The origamics logo. 6.2. Folding a piece of paper by concentrating the four vertices at one point. 6.3. Remarks on polygonal figures of type n. 6.4. An approach to the problem using group study. 6.5. Reducing the work of paper folding; one eighth of the square will do. 6.6. Why does the petal pattern appear? 6.7. What are the areas of the regions? -- 7. Heptagon regions exist? 7.1. Review of the folding procedure. 7.2. A heptagon appears! 7.3. Experimenting with rectangles with different ratios of sides. 7.4. Try a rhombus -- 8. A wonder of eleven stars. 8.1. Experimenting with paper folding. 8.2. Discovering. 8.3. Proof. 8.4. Morer revelations regarding the intersections of the extensions of the creases. 8.5. Proof of the observation on the intersection points of extended edge-to-line creases. 8.6. The joy of discovering and the excitement of further searching. 10. Inspiration from rectangular paper. 10.1. A scenario: the stern king of Origami Land. 10.2. Begin with a simpler problem: how to divide the rectangle horizontally and vertically into 3 equal parts. 10.3. A 5-parts division point; the pendulum idea helps. 10.4. A method for finding a 7-parts division point. 10.5. The investigation continues: try the pendulum idea on the 7-parts division method. 10.6. The search for 11-parts and 13-parts division point. 10.7. Another method for finding 11-parts and 13-parts division points. 10.8. Continue the trend of thought: 15-parts and 17-parts division points. 10.9. Some ideas related to the ratios for equal-parts division based on similar triangles. 10.10. Towards more division parts. 10.11. Generalizing to all rectangles. Origami. http://id.loc.gov/authorities/subjects/sh85095643 Polyhedra Models. http://id.loc.gov/authorities/subjects/sh85104648 Origami. Polyèdres Modèles. GAMES Sudoku. bisacsh MATHEMATICS Recreations & Games. bisacsh Origami fast Polyhedra Models fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85095643 http://id.loc.gov/authorities/subjects/sh85104648 |
| title | Origamics : mathematical explorations through paper folding / |
| title_alt | Origamikusu. |
| title_auth | Origamics : mathematical explorations through paper folding / |
| title_exact_search | Origamics : mathematical explorations through paper folding / |
| title_full | Origamics : mathematical explorations through paper folding / Kazuo Haga ; edited and translated by Josefina C. Fonacier, Masami Isoda. |
| title_fullStr | Origamics : mathematical explorations through paper folding / Kazuo Haga ; edited and translated by Josefina C. Fonacier, Masami Isoda. |
| title_full_unstemmed | Origamics : mathematical explorations through paper folding / Kazuo Haga ; edited and translated by Josefina C. Fonacier, Masami Isoda. |
| title_short | Origamics : |
| title_sort | origamics mathematical explorations through paper folding |
| title_sub | mathematical explorations through paper folding / |
| topic | Origami. http://id.loc.gov/authorities/subjects/sh85095643 Polyhedra Models. http://id.loc.gov/authorities/subjects/sh85104648 Origami. Polyèdres Modèles. GAMES Sudoku. bisacsh MATHEMATICS Recreations & Games. bisacsh Origami fast Polyhedra Models fast |
| topic_facet | Origami. Polyhedra Models. Polyèdres Modèles. GAMES Sudoku. MATHEMATICS Recreations & Games. Origami Polyhedra Models |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=521237 |
| work_keys_str_mv | AT hagakazuo origamikusu AT fonacierjosefina origamikusu AT isodamasami origamikusu AT hagakazuo origamicsmathematicalexplorationsthroughpaperfolding AT fonacierjosefina origamicsmathematicalexplorationsthroughpaperfolding AT isodamasami origamicsmathematicalexplorationsthroughpaperfolding |