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1 | (28) |
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1.1 Setting the Scene: Which Instrument Is Stronger? |
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1 | (4) |
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1.2 Marginalization and Its Epistemological Consequences |
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5 | (5) |
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1.3 Marginalization and the Medium: Or---Why Did Marginalization Occur? |
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10 | (5) |
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1.4 The Economy of Excess and Lack |
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15 | (4) |
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1.5 Historiographical Perspectives and an Overview |
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19 | (10) |
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1.5.1 Marginalized Traditions |
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20 | (2) |
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1.5.2 The Historical Research to Date and Overview |
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22 | (2) |
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1.5.3 Argument and Structure |
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24 | (5) |
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2 From the Sixteenth Century Onwards: Folding Polyhedra---New Epistemological Horizons? |
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29 | (64) |
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30 | (18) |
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2.1.1 Underweysung der Messung and the Unfolded Nets |
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32 | (7) |
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2.1.2 Folded Tiles and Folds of Drapery |
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39 | (5) |
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2.1.3 Durer's Folding: An Epistemological Offer? |
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44 | (4) |
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2.2 Durer's Unfolded Polyhedra: Context and Ramifications |
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48 | (35) |
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2.2.1 Pacioli and Bovelles, Paper Instruments and Folded Books: Encounters of Folding and Geometry |
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49 | (4) |
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2.2.1.1 Paper Instruments: Folding for Science |
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53 | (6) |
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2.2.1.2 A Historical Detour: Bat Books and Imposition of the Book---The Standardization of Folding |
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59 | (7) |
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2.2.2 Durer's Followers Fold a Net |
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66 | (10) |
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2.2.2.1 Stevin's and Cowley's Impossible Nets |
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76 | (4) |
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2.2.2.2 Nets of Polyhedra: A Mathematical Stagnation? |
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80 | (3) |
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2.3 Ignoring Folding as a Method of Proof in Mathematics |
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83 | (10) |
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2.3.1 Folding and Geometry: A Forgotten Beginning---Pacioli Folds a Gnomon |
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83 | (3) |
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2.3.2 Folding and Geometry: A Problematic Beginning |
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86 | (7) |
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3 Prolog to the Nineteenth Century: Accepting Folding as a Method of Inference |
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93 | (178) |
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3.1 Folding and the Parallel Postulate |
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94 | (4) |
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3.1.1 Folding and Parallel Line: An Implicit Encounter During the Arabic Middle Ages |
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94 | (2) |
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3.1.2 Folding and Parallel Line: An Explicit Encounter During the Eighteenth Century |
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96 | (2) |
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3.2 Folding in Proofs: Suzanne and Francceur |
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98 | (6) |
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3.2.1 Symmetry and Folding Diderot and Symmetry in Francceur's Cours Complet |
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100 | (4) |
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3.3 Lardner, Wright, Henrici: Symmetry with Folding in Great Britain |
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104 | (9) |
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4 The Nineteenth Century: What Can and Cannot Be (Re)presented---On Models and Kindergartens |
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113 | (1) |
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4.1 On Models in General and Folded Models in Particular |
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114 | (92) |
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4.1.1 Mathematical Models During the Eighteenth and Nineteenth Centuries |
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115 | (11) |
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4.1.2 Folded Models in Mathematics: Dupin, Schlegel, Beltrami, Schwarz and the Two Wieners |
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126 | (1) |
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4.1.2.1 Louis Dupin and Victor Schlegel: How to Fold Nets in the Nineteenth Century |
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126 | (15) |
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4.1.2.2 Eugenio Beltrami and Models in Italy |
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141 | (11) |
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4.1.2.3 Schwarz, Peano and Christian Wiener |
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152 | (13) |
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165 | (15) |
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4.1.3 A Detour into the Realm of Chemistry: The Folded Models of Van't Hoff and Sachse |
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180 | (1) |
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4.1.3.1 Van't Hoff Folds a Letter |
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181 | (13) |
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4.1.3.2 Hermann Sachse's Three Equations |
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194 | (6) |
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4.1.3.3 Folded Models in Chemistry and Mathematics: A Failed Encounter |
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200 | (3) |
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4.1.4 Modeling with the Fold: A Minority Inside a Vanished Tradition |
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203 | (3) |
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4.2 Folding in Kindergarten: How Children's Play Entered the Mathematical Scene |
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206 | (65) |
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207 | (2) |
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4.2.1.1 Frobel and Mathematics |
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209 | (7) |
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216 | (11) |
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4.2.1.3 Frobel's Influence and the Vanishing of Folding-Based Mathematics from Kindergarten |
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227 | (20) |
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4.2.2 From Great Britain to India |
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247 | (3) |
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4.2.2.1 First Lessons in Geometry: Bhimanakunte Hanumantha Rao's Book |
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250 | (4) |
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4.2.2.2 The Books of Tandalam Sundara Row |
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254 | (14) |
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4.2.3 Folding in Kindergartens: A Successful Marginalization |
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268 | (3) |
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5 The Twentieth Century: Towards the Axiomatization, Operationalization and Algebraization of the Fold |
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271 | (84) |
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5.1 The Influence of Row's Book |
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272 | (46) |
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5.1.1 First Steps Towards Operative Axiomatization: Ahrens, Hurwitz, Rupp |
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273 | (1) |
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5.1.1.1 Anhrens's Fundamental Folding Constructions |
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274 | (4) |
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5.1.1.2 The Basic Operations of Adolf Hurwitz |
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278 | (4) |
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5.1.1.3 Lotka and Rupp: Creases as Envelopes |
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282 | (3) |
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5.1.2 The Distinction Between Axioms and Operations: A Book by Young and Young |
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285 | (1) |
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5.1.2.1 The Youngs's The First Book of Geometry |
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286 | (7) |
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5.1.2.2 Translations and Acceptance |
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293 | (2) |
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5.1.3 A Detour: How Does One Fold a Pentagon? |
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295 | (1) |
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5.1.3.1 The Construction of Euclid |
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296 | (1) |
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5.1.3.2 How Does One Fold a Regular Pentagon? |
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297 | (8) |
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5.1.3.3 How Does One Knot a Regular Pentagon? |
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305 | (13) |
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5.2 An Algebraic Entwinement of Theory and Praxis: Beloch's Fold |
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318 | (22) |
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5.2.1 Vacca's 1930 Manuscript |
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319 | (4) |
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5.2.2 Beloch's 1934 Discoveries |
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323 | (4) |
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5.2.3 After 1934: Further Development and Reception |
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327 | (3) |
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5.2.3.1 Lill's Method of Solving Any Equation |
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330 | (6) |
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5.2.3.2 A Fall Towards Oblivion? |
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336 | (4) |
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5.3 Epilog for the Twentieth Century: The Folding of Algebraic Symbols |
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340 | (15) |
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5.3.1 The Faltung of Bilinear Forms |
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341 | (9) |
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5.3.2 Convolution as Faltung |
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350 | (5) |
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6 Coda: 1989---The Axiomatization(s) of the Fold |
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355 | (22) |
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6.1 The Operations of Humiaki Huzita |
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358 | (5) |
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6.2 The Operations of Jacques Justin |
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363 | (5) |
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6.3 Conclusion: Too-Much, Too-Little---Unfolding an Epistemological Non-equilibrium |
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368 | (9) |
| Appendix A Margherita Beloch Piazzolla: "Alcune applicazioni del metodo del ripiegamento della carta di Sundara Row" |
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377 | (4) |
| Appendix B Deleuze, Leibniz and the Unmathematical Fold |
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381 | (8) |
| References |
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389 | (26) |
| Index |
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415 | |
