Acknowledgments |
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xv | |
Preface |
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xvii | |
Introduction |
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xxi | |
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1 Nineteenth-Century Science Breakthroughs in Europe: Historical Background |
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1 | (72) |
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1.1 Timeline of Key Historical Events in Central Europe of the 18th/19th Century |
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4 | (58) |
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1.2 The 19th-century German Ideal of Scientific Education |
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62 | (11) |
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1.2.1 Educational Concepts in 19th-century Central Europe |
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63 | (2) |
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1.2.2 Between "Bildung" and "Wissenschaft" in Higher Education |
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65 | (8) |
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2 A. F. Mobius: The Time of His Early Life and Academic Education (1790-1815) |
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73 | (42) |
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2.1 August Ferdinand Mobius and the World He Lived in as a Young Boy and School Student |
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75 | (16) |
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2.1.1 Childhood of August Ferdinand Mobius (1790-1803) |
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83 | (2) |
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2.1.2 August Ferdinand Mobius's Time as School Student in Schulpforta (1803-09) |
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85 | (6) |
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2.2 August Ferdinand Mobius and the World He Lived in as University Student |
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91 | (24) |
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2.2.1 A. F. Mobius's Time in Leipzig (1809-13) |
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94 | (3) |
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2.2.2 A. F. Mobius's Time in Gottingen and Halle (1813-15) |
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97 | (1) |
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97 | (7) |
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104 | (7) |
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2.2.3 A. F. Mobius Back at Leipzig University (1815) |
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111 | (4) |
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3 A. F. Mobius: The Time of His Academic Career (1815-68) |
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115 | (82) |
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3.1 A. F. Mobius's Living Situation in Leipzig |
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117 | (5) |
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3.2 A. F. Mobius's Professorship Offers from Outside Saxony |
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122 | (1) |
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3.3 A. F. Mobius's Teaching Activities at Leipzig University |
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123 | (1) |
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3.4 The Leipzig Observatory |
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124 | (3) |
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3.5 A. F. Mobius's Scientific Oeuvre and Publications |
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127 | (17) |
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128 | (6) |
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134 | (10) |
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3.6 A. F. Mobius's Friendship with Hermann Gunther Grassmann |
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144 | (6) |
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3.7 A. F. Mobius's Friendship with Gustav Theodor Fechner |
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150 | (6) |
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156 | (6) |
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3.9 Development of Mobius's Conditions of Living |
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162 | (2) |
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3.10 Academic Distinctions and Honors of August Ferdinand Mobius--and His Obituary |
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164 | (4) |
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3.11 Short Extraction from the Family Saga of August Ferdinand Mobius |
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168 | (6) |
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3.12 A. F. Mobius's Relationship to Politics |
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174 | (23) |
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4 During the Napoleonic Wars in Europe: Eyewitnesses and Victims |
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197 | (46) |
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4.1 Testimonies from Contemporary Witnesses of the Napoleonic Wars in Europe (1806-15) |
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199 | (23) |
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4.1.1 Madrid Guerilla Fighting the Napoleonic Invasion |
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199 | (2) |
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4.1.2 Napoleonic Siege of Vienna and Beethoven's Dread of Cannon Thunder |
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201 | (4) |
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4.1.3 From Naumburg to Schonbrunn: A Failed Attempt of Napoleon's Assassination |
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205 | (4) |
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4.1.4 The Battle of Dresden (August 26-27, 1813) |
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209 | (3) |
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4.1.5 The Battle of the Nations in Leipzig (October 16-19, 1813) |
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212 | (6) |
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4.1.6 Eyewitnesses of the Battle of the Nations as Documented in the Stadtarchiv Leipzig [ 3] |
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218 | (4) |
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4.2 The Mount Tambora Volcano Eruption in April 1815 |
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222 | (21) |
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5 Mobius Strip Topology and More: Elaborations on Mathematics |
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243 | (108) |
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5.1 Mathematical Representations of the Mobius Strip |
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249 | (3) |
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5.2 Calculation of the "Developable" Shape of the Mobius Strip |
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252 | (4) |
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5.3 More about Topology in a Nutshell |
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256 | (21) |
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5.3.1 Mobius Strip: An Example of Algebraic Surgery |
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258 | (2) |
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5.3.2 From the Mobius Strip to the Klein Bottle: The Rectangle Peg Problem Solved in 2020 |
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260 | (17) |
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5.4 Euler's Polyhedron Formula: The Euler Characteristic of Convex Polyhedra without a Hole |
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277 | (5) |
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5.5 The Power of Euler's Formula |
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282 | (1) |
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283 | (2) |
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5.7 The Platonic Bodies in Philosophy |
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285 | (7) |
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5.8 Generalizations of the Euler Formula for Polyhedra with Holes |
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292 | (4) |
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5.8.1 Generalization by L'Huilier |
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292 | (2) |
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5.8.2 The Euler-Poincare Formula |
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294 | (2) |
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5.9 More on Topology of Twisted Closed Band Objects: Their Linking, Twist, and Writhe Numbers |
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296 | (1) |
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5.10 The Mobius Transformations |
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296 | (4) |
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5.11 The Mobius Tetrahedra |
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300 | (1) |
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5.12 The Mobius Function, u(n) |
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301 | (3) |
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5.13 The Fibonacci Spiral and the Mobius Strip |
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304 | (3) |
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5.14 The Golden Section and the Fibonacci Spiral Geometry |
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307 | (3) |
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5.15 Constructing the Golden Rectangle according to the Golden Ratio |
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310 | (1) |
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5.16 Spinor Property of the Mobius Strip |
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311 | (5) |
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5.17 Utilizing the Spinor Property of Protons to Spectacularly Enhance the ENDOR Effect |
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316 | (3) |
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5.18 Outlook: Quantum Computing with Spin 1/2 Spinor Systems |
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319 | (32) |
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5.18.1 Schrodinger's Cat Paradoxon |
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326 | (3) |
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5.18.2 Progress in Quantum Computing |
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329 | (2) |
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5.18.3 Future Prospects for Large-Scale Quantum Computing |
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331 | (20) |
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6 A. F. Mobius and His Time: Elaborations on Astronomy |
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351 | (210) |
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6.1 The 18th/19th Centuries Scientific Renaissance and Astronomical Revolution in Germany |
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353 | (6) |
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6.2 German Astronomical Instrumentation of the 18th and 19th Centuries |
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359 | (2) |
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6.3 Fraunhofer's Refracting Telescopes |
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361 | (6) |
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6.4 Astronomical Discoveries by A. F. Mobius's Contemporaries and Their Instrumentation |
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367 | (128) |
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6.4.1 Carl Friedrich Gauss (1777-1855) |
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369 | (22) |
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6.4.1.1 C. F. Gauss, A. von Humboldt, W. Weber, A. F. Mobius, an unparalleled quartet in 19th century science |
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391 | (21) |
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6.4.1.2 The 2019 anniversaries of A. von Humboldt, C. F. Gauss, and A. F. Mobius, and the latest news on Earth's magnetic field variations |
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412 | (6) |
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6.4.2 Friedrich Wilhelm Argelander (1799-1875) |
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418 | (7) |
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6.4.3 Friedrich Wilhelm Bessel (1784-1846) |
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425 | (1) |
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6.4.3.1 Friedrich Wilhelm Bessel at the Observatories of Lilienthal (1806-10) and Konigsberg (1810-46) |
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426 | (9) |
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6.4.3.2 Friedrich Wilhelm Bessel and the prediction of eclipses |
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435 | (3) |
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6.4.3.3 Solar eclipse of May 29, 1919, and the first test of Einstein's relativity theory |
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438 | (10) |
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6.4.3.4 The "Einstein Myth" and a few questions asked by critical science historians |
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448 | (6) |
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6.4.3.5 Newtonian calculations of light deflections by celestial masses, Johann Georg von Soldner (1776-1833), and the banishing of Einstein's relativity theory by Nazi Germany |
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454 | (5) |
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6.4.4 Johann Elert Bode (1747-1826) |
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459 | (4) |
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6.4.5 Johann Franz Encke (1791-1865) |
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463 | (4) |
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6.4.6 Johann Gottfried Galle (1812-1910) |
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467 | (3) |
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6.4.7 Karl Ludwig Harding (1765-1834) |
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470 | (1) |
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6.4.8 Friedrich Wilhelm Herschel (1738-1822) and Caroline Herschel (1750-1848) |
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471 | (9) |
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6.4.9 Heinrich Wilhelm Matthias Olbers (1758-1840) |
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480 | (3) |
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6.4.10 Johann Hieronymus Schroeter (1745-1816) |
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483 | (9) |
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6.4.11 Friedrich Georg Wilhelm von Struve (1793-1864) |
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492 | (2) |
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6.4.12 Franz Xaver von Zach (1754-1832) |
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494 | (1) |
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6.5 August Ferdinand Mobius's Activities as Astronomer in Leipzig |
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495 | (1) |
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6.6 Honors in Remembrance of August Ferdinand Mobius |
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496 | (4) |
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6.7 News (2018) from the NASA Lunar Reconnaissance Orbiter (LRO) Mission |
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500 | (5) |
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6.7.1 NASA History and the History of US Civilian-Military Relations in Space |
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500 | (2) |
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6.7.2 The NASA Lunar Reconnaissance Orbiter (LRO) Mission |
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502 | (3) |
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6.8 Breaking News (December 08, 2018) from The New York Times: China Launched the First-Ever Surface Mission ("Chang'e 4") to the Moon's Far Side |
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505 | (19) |
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6.8.1 Breaking News (December 2020) from China's "Chang'e 5 Moon Mission" which Collected and Brought 2 Kg of Rock Samples from the Moon's Surface Back to Earth |
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510 | (5) |
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6.8.2 Fifty Years Anniversary Celebrations (2019) of the Apollo 11 Mission, First Man on the Moon |
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515 | (2) |
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6.8.3 Postscriptum to the Apollo 11 Mission, First Man on the Moon |
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517 | (7) |
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6.9 News (2016) about Space-Based Infrared Telescope Probe Rosetta and Its Long Journey to the Comet Churyumov-Gerasimenko |
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524 | (6) |
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6.10 Breaking News (2019): Saturn's Rings and Moons Revealed in Unprecedented Detail by Cassini Spacecraft Telescopes and Mass Spectrometers |
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530 | (10) |
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6.10.1 Breaking News (2019): Saturn's Rings as Unveiled by Cassini |
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532 | (4) |
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6.10.2 Breaking News (2019): Saturn's Moons Titan and Enceladus as Unveiled by Cassini |
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536 | (4) |
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6.11 Evidence from the Herschel Space Observatory of a Twisted Ring Structure of Dense Galactic Matter Orbiting the Center of the Milky Way |
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540 | (8) |
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6.12 Breaking News from November 13, 2019: The James Webb Space Telescope is Finally Ready |
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548 | (13) |
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7 Mobius Strip Topology: Applications from Chemistry |
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561 | (110) |
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7.1 Erich Hiickel and His Molecular Orbital Concept of Aromaticity in Organic Chemistry |
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561 | (7) |
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7.2 Brief Historical Overview of the Development of Quantum Chemistry in Germany |
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568 | (15) |
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7.2.1 Development before World War II |
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568 | (4) |
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7.2.2 Development after World War II |
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572 | (5) |
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7.2.3 The Tragic Story of Hans Hellmann |
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577 | (6) |
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7.3 Edgar Heilbronner and his MO Concept of Mobius Aromaticity in Organic Chemistry |
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583 | (10) |
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7.3.1 Edgar Heilbronner: The Man of Science |
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584 | (2) |
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7.3.2 Edgar Heilbronner: The Man of Culture |
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586 | (7) |
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7.4 Topology of Twisted Ribbon Molecules, the DNA Example |
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593 | (2) |
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7.5 Quantifying the Topology of Twisted Molecules: Twist, Writhe, and Linking Number |
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595 | (9) |
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7.6 Examples of Molecules with Mobius Strip Topology |
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604 | (9) |
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7.6.1 Aromatic Mobius Strip Molecules: Annulene Systems |
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605 | (6) |
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7.6.2 Aromatic Mobius Strip Molecules: Expanded Porphyrin Systems |
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611 | (2) |
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7.7 Basics about NMR, EPR, and ENDOR Spectroscopies at High Magnetic Fields |
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613 | (6) |
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7.7.1 NMR versus EPR Spectroscopy at High Magnetic Fields |
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614 | (4) |
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7.7.2 ENDOR at High Magnetic Fields |
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618 | (1) |
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7.8 Recent EPR Experiments on Mobius-Type Expanded Porphyrin Molecules |
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619 | (21) |
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7.8.1 Mobius-Huckel Topology Switching in Expanded Porphyrins: EPR, ENDOR, and DFT Studies of Doublet and Triplet Open-Shell Systems |
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620 | (1) |
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621 | (5) |
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626 | (2) |
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628 | (1) |
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7.8.1.4 Results and Discussion |
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629 | (11) |
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7.9 Cyclotides as Example of Cyclic Proteins with Trefoil Knot and Mobius Strip Topology |
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640 | (31) |
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7.9.1 More about Knot Topology of Lines in Relation to Mobius Strip Topology of Surfaces |
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647 | (4) |
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7.9.2 Cyclotides in Medical Therapy Applications |
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651 | (2) |
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7.9.3 Oral Activity of a Nature-Derived Cyclic Peptide for the Treatment of Multiple Sclerosis |
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653 | (18) |
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8 The Mobius Strip Topology: Applications from Physics and Nanomaterials |
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671 | (46) |
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8.1 Quantization of the Hall Effect |
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678 | (7) |
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8.2 A Primer on Topological Insulators |
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685 | (5) |
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8.3 Graphene-Based Topological Insulators |
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690 | (5) |
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8.4 Spin States of Mobius Graphene Nanoribbons |
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695 | (4) |
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8.5 Designing Topological Insulators from Graphene Nanoribbons |
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699 | (8) |
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8.6 Laser Pulses Create Topological State in Graphene |
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707 | (10) |
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9 Mobius Strip Topology: Highlights from the Arts and Architecture |
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717 | (154) |
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9.1 Mobius Strips before Mobius: By the Example of Baroque Music |
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719 | (7) |
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9.2 Pre-M6bius One-Sidedness: By the Example of Visual Arts and Architecture |
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726 | (2) |
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9.3 More Twisted Bands from Roman Mosaics, the Ouroboros and Infinity |
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728 | (3) |
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9.4 Mathematics and Architecture, Symmetry and Beauty in the Arts and Sciences |
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731 | (33) |
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9.4.1 Influence of Mathematics on Art and Architecture over the Centuries |
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732 | (1) |
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9.4.2 Symmetry and Beauty |
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733 | (14) |
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9.4.2.1 Interplay of Aesthetics and Science |
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747 | (3) |
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9.4.2.2 Symmetry and Architecture |
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750 | (6) |
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9.4.2.3 Symmetry and Poetry |
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756 | (8) |
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9.5 Mobius Strip Topology in Literature, Theater, and Film |
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764 | (33) |
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9.5.1 "La Banda de Moebius" Theater Play by Antonio Toga, Neza (Mexico City), 2020 |
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766 | (3) |
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9.5.2 "The Parallel World," Theater Play about People in the Quantum World, a Twin Production by Kay Voges in Berlin and Dortmund, 2018 |
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769 | (4) |
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9.5.3 "The Bald Soprano," Theater Play by Eugene Ionesco, 1950 |
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773 | (4) |
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9.5.4 "Kata-Omoi" ("One-Sided Love"), Mystery Novel by Keigo Higashino, 2001 |
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777 | (5) |
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9.5.5 "A Subway Named Mobius," Short Story by Armin Joseph Deutsch, 1950, and "Moebius," a Film by Gustavo Daniel Mosquera R, 1996 |
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782 | (13) |
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9.5.6 "Mobius," Film by Eric Rochant, 2013 |
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795 | (2) |
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9.6 Mobius Topology in Sculpture |
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797 | (15) |
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9.6.1 Max Bill (1908-94), Switzerland |
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797 | (5) |
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9.6.2 Keizo Ushio (Born 1951), Japan |
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802 | (5) |
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9.6.3 Robert R. Wilson (1914-2000), the United States |
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807 | (5) |
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9.7 Mobius Strip Topology: Highlights from Modern Architecture |
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812 | (59) |
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9.7.1 A Fundamental Problem of Architecture when Designing Buildings in Three-Dimensional Space with Several Floors Interconnected by a Mobius Strip Surface |
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818 | (5) |
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9.7.2 Max Reinhardt Haus in Berlin by Peter Eisenman (1992) |
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823 | (21) |
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9.7.3 Mobius House at Het Gooi Near Amsterdam by Ben van Berkel, 1993 |
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844 | (7) |
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9.7.4 Phoenix International Media Center in Beijing by Shao Weiping, 2004 |
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851 | (11) |
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9.7.5 Lucky Knot Bridge in Changsha (China) by NEXT Architects with their Chief Architects John van de Water (Dutch) and Jiang Xiaofei (Chinese), 2013 |
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862 | (9) |
Index |
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871 | |