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E-raamat: Möbius Strip Topology: History, Science, and Applications in Nanotechnology, Materials, and the Arts [Taylor & Francis e-raamat]

  • Formaat: 886 pages, 4 Tables, black and white; 86 Line drawings, color; 20 Line drawings, black and white; 87 Halftones, color; 95 Halftones, black and white; 173 Illustrations, color; 115 Illustrations, black and white
  • Ilmumisaeg: 30-Nov-2022
  • Kirjastus: Jenny Stanford Publishing
  • ISBN-13: 9781003256298
  • Taylor & Francis e-raamat
  • Hind: 286,20 €*
  • * hind, mis tagab piiramatu üheaegsete kasutajate arvuga ligipääsu piiramatuks ajaks
  • Tavahind: 408,86 €
  • Säästad 30%
  • Formaat: 886 pages, 4 Tables, black and white; 86 Line drawings, color; 20 Line drawings, black and white; 87 Halftones, color; 95 Halftones, black and white; 173 Illustrations, color; 115 Illustrations, black and white
  • Ilmumisaeg: 30-Nov-2022
  • Kirjastus: Jenny Stanford Publishing
  • ISBN-13: 9781003256298
In the 19th century, pure mathematics research reached a climax in Germany, and Carl Friedrich Gauss (17771855) was an epochal example. August Ferdinand Möbius (17901868) was his doctoral student whose work was profoundly influenced by him. In the 18th century, it had been mostly the French school of applied mathematics that enabled the rapid developments of science and technology in Europe. How could this shift happen? It can be argued that the major reasons were the devastating consequences of the Napoleonic Wars in Central Europe, leading to the total defeat of Prussia in 1806. Immediately following, far-reaching reforms of the entire state system were carried out in Prussia and other German states, also affecting the educational system. It now guaranteed freedom of university teaching and research. This attracted many creative people with new ideas enabling the golden age of pure mathematics and fundamental theory in physical sciences.

Möbius legacy reaches far into todays sciences, arts, and architecture. The famous one-sided Möbius strip is a paradigmatic example of the ongoing fascination with mathematical topology. This is the first book to present numerous detailed case studies on Möbius topology in science and the humanities. It is written for those who believe in the power of ideas in our culture, experts and laymen alike.
Acknowledgments xv
Preface xvii
Introduction xxi
1 Nineteenth-Century Science Breakthroughs in Europe: Historical Background
1(72)
1.1 Timeline of Key Historical Events in Central Europe of the 18th/19th Century
4(58)
1.2 The 19th-century German Ideal of Scientific Education
62(11)
1.2.1 Educational Concepts in 19th-century Central Europe
63(2)
1.2.2 Between "Bildung" and "Wissenschaft" in Higher Education
65(8)
2 A. F. Mobius: The Time of His Early Life and Academic Education (1790-1815)
73(42)
2.1 August Ferdinand Mobius and the World He Lived in as a Young Boy and School Student
75(16)
2.1.1 Childhood of August Ferdinand Mobius (1790-1803)
83(2)
2.1.2 August Ferdinand Mobius's Time as School Student in Schulpforta (1803-09)
85(6)
2.2 August Ferdinand Mobius and the World He Lived in as University Student
91(24)
2.2.1 A. F. Mobius's Time in Leipzig (1809-13)
94(3)
2.2.2 A. F. Mobius's Time in Gottingen and Halle (1813-15)
97(1)
2.2.2.1 In Gottingen
97(7)
2.2.2.2 In Halle
104(7)
2.2.3 A. F. Mobius Back at Leipzig University (1815)
111(4)
3 A. F. Mobius: The Time of His Academic Career (1815-68)
115(82)
3.1 A. F. Mobius's Living Situation in Leipzig
117(5)
3.2 A. F. Mobius's Professorship Offers from Outside Saxony
122(1)
3.3 A. F. Mobius's Teaching Activities at Leipzig University
123(1)
3.4 The Leipzig Observatory
124(3)
3.5 A. F. Mobius's Scientific Oeuvre and Publications
127(17)
3.5.1 Astronomy
128(6)
3.5.2 Mathematics
134(10)
3.6 A. F. Mobius's Friendship with Hermann Gunther Grassmann
144(6)
3.7 A. F. Mobius's Friendship with Gustav Theodor Fechner
150(6)
3.8 The Mobius Strip
156(6)
3.9 Development of Mobius's Conditions of Living
162(2)
3.10 Academic Distinctions and Honors of August Ferdinand Mobius--and His Obituary
164(4)
3.11 Short Extraction from the Family Saga of August Ferdinand Mobius
168(6)
3.12 A. F. Mobius's Relationship to Politics
174(23)
4 During the Napoleonic Wars in Europe: Eyewitnesses and Victims
197(46)
4.1 Testimonies from Contemporary Witnesses of the Napoleonic Wars in Europe (1806-15)
199(23)
4.1.1 Madrid Guerilla Fighting the Napoleonic Invasion
199(2)
4.1.2 Napoleonic Siege of Vienna and Beethoven's Dread of Cannon Thunder
201(4)
4.1.3 From Naumburg to Schonbrunn: A Failed Attempt of Napoleon's Assassination
205(4)
4.1.4 The Battle of Dresden (August 26-27, 1813)
209(3)
4.1.5 The Battle of the Nations in Leipzig (October 16-19, 1813)
212(6)
4.1.6 Eyewitnesses of the Battle of the Nations as Documented in the Stadtarchiv Leipzig [ 3]
218(4)
4.2 The Mount Tambora Volcano Eruption in April 1815
222(21)
5 Mobius Strip Topology and More: Elaborations on Mathematics
243(108)
5.1 Mathematical Representations of the Mobius Strip
249(3)
5.2 Calculation of the "Developable" Shape of the Mobius Strip
252(4)
5.3 More about Topology in a Nutshell
256(21)
5.3.1 Mobius Strip: An Example of Algebraic Surgery
258(2)
5.3.2 From the Mobius Strip to the Klein Bottle: The Rectangle Peg Problem Solved in 2020
260(17)
5.4 Euler's Polyhedron Formula: The Euler Characteristic of Convex Polyhedra without a Hole
277(5)
5.5 The Power of Euler's Formula
282(1)
5.6 The Platonic Bodies
283(2)
5.7 The Platonic Bodies in Philosophy
285(7)
5.8 Generalizations of the Euler Formula for Polyhedra with Holes
292(4)
5.8.1 Generalization by L'Huilier
292(2)
5.8.2 The Euler-Poincare Formula
294(2)
5.9 More on Topology of Twisted Closed Band Objects: Their Linking, Twist, and Writhe Numbers
296(1)
5.10 The Mobius Transformations
296(4)
5.11 The Mobius Tetrahedra
300(1)
5.12 The Mobius Function, u(n)
301(3)
5.13 The Fibonacci Spiral and the Mobius Strip
304(3)
5.14 The Golden Section and the Fibonacci Spiral Geometry
307(3)
5.15 Constructing the Golden Rectangle according to the Golden Ratio
310(1)
5.16 Spinor Property of the Mobius Strip
311(5)
5.17 Utilizing the Spinor Property of Protons to Spectacularly Enhance the ENDOR Effect
316(3)
5.18 Outlook: Quantum Computing with Spin 1/2 Spinor Systems
319(32)
5.18.1 Schrodinger's Cat Paradoxon
326(3)
5.18.2 Progress in Quantum Computing
329(2)
5.18.3 Future Prospects for Large-Scale Quantum Computing
331(20)
6 A. F. Mobius and His Time: Elaborations on Astronomy
351(210)
6.1 The 18th/19th Centuries Scientific Renaissance and Astronomical Revolution in Germany
353(6)
6.2 German Astronomical Instrumentation of the 18th and 19th Centuries
359(2)
6.3 Fraunhofer's Refracting Telescopes
361(6)
6.4 Astronomical Discoveries by A. F. Mobius's Contemporaries and Their Instrumentation
367(128)
6.4.1 Carl Friedrich Gauss (1777-1855)
369(22)
6.4.1.1 C. F. Gauss, A. von Humboldt, W. Weber, A. F. Mobius, an unparalleled quartet in 19th century science
391(21)
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
412(6)
6.4.2 Friedrich Wilhelm Argelander (1799-1875)
418(7)
6.4.3 Friedrich Wilhelm Bessel (1784-1846)
425(1)
6.4.3.1 Friedrich Wilhelm Bessel at the Observatories of Lilienthal (1806-10) and Konigsberg (1810-46)
426(9)
6.4.3.2 Friedrich Wilhelm Bessel and the prediction of eclipses
435(3)
6.4.3.3 Solar eclipse of May 29, 1919, and the first test of Einstein's relativity theory
438(10)
6.4.3.4 The "Einstein Myth" and a few questions asked by critical science historians
448(6)
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
454(5)
6.4.4 Johann Elert Bode (1747-1826)
459(4)
6.4.5 Johann Franz Encke (1791-1865)
463(4)
6.4.6 Johann Gottfried Galle (1812-1910)
467(3)
6.4.7 Karl Ludwig Harding (1765-1834)
470(1)
6.4.8 Friedrich Wilhelm Herschel (1738-1822) and Caroline Herschel (1750-1848)
471(9)
6.4.9 Heinrich Wilhelm Matthias Olbers (1758-1840)
480(3)
6.4.10 Johann Hieronymus Schroeter (1745-1816)
483(9)
6.4.11 Friedrich Georg Wilhelm von Struve (1793-1864)
492(2)
6.4.12 Franz Xaver von Zach (1754-1832)
494(1)
6.5 August Ferdinand Mobius's Activities as Astronomer in Leipzig
495(1)
6.6 Honors in Remembrance of August Ferdinand Mobius
496(4)
6.7 News (2018) from the NASA Lunar Reconnaissance Orbiter (LRO) Mission
500(5)
6.7.1 NASA History and the History of US Civilian-Military Relations in Space
500(2)
6.7.2 The NASA Lunar Reconnaissance Orbiter (LRO) Mission
502(3)
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
505(19)
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
510(5)
6.8.2 Fifty Years Anniversary Celebrations (2019) of the Apollo 11 Mission, First Man on the Moon
515(2)
6.8.3 Postscriptum to the Apollo 11 Mission, First Man on the Moon
517(7)
6.9 News (2016) about Space-Based Infrared Telescope Probe Rosetta and Its Long Journey to the Comet Churyumov-Gerasimenko
524(6)
6.10 Breaking News (2019): Saturn's Rings and Moons Revealed in Unprecedented Detail by Cassini Spacecraft Telescopes and Mass Spectrometers
530(10)
6.10.1 Breaking News (2019): Saturn's Rings as Unveiled by Cassini
532(4)
6.10.2 Breaking News (2019): Saturn's Moons Titan and Enceladus as Unveiled by Cassini
536(4)
6.11 Evidence from the Herschel Space Observatory of a Twisted Ring Structure of Dense Galactic Matter Orbiting the Center of the Milky Way
540(8)
6.12 Breaking News from November 13, 2019: The James Webb Space Telescope is Finally Ready
548(13)
7 Mobius Strip Topology: Applications from Chemistry
561(110)
7.1 Erich Hiickel and His Molecular Orbital Concept of Aromaticity in Organic Chemistry
561(7)
7.2 Brief Historical Overview of the Development of Quantum Chemistry in Germany
568(15)
7.2.1 Development before World War II
568(4)
7.2.2 Development after World War II
572(5)
7.2.3 The Tragic Story of Hans Hellmann
577(6)
7.3 Edgar Heilbronner and his MO Concept of Mobius Aromaticity in Organic Chemistry
583(10)
7.3.1 Edgar Heilbronner: The Man of Science
584(2)
7.3.2 Edgar Heilbronner: The Man of Culture
586(7)
7.4 Topology of Twisted Ribbon Molecules, the DNA Example
593(2)
7.5 Quantifying the Topology of Twisted Molecules: Twist, Writhe, and Linking Number
595(9)
7.6 Examples of Molecules with Mobius Strip Topology
604(9)
7.6.1 Aromatic Mobius Strip Molecules: Annulene Systems
605(6)
7.6.2 Aromatic Mobius Strip Molecules: Expanded Porphyrin Systems
611(2)
7.7 Basics about NMR, EPR, and ENDOR Spectroscopies at High Magnetic Fields
613(6)
7.7.1 NMR versus EPR Spectroscopy at High Magnetic Fields
614(4)
7.7.2 ENDOR at High Magnetic Fields
618(1)
7.8 Recent EPR Experiments on Mobius-Type Expanded Porphyrin Molecules
619(21)
7.8.1 Mobius-Huckel Topology Switching in Expanded Porphyrins: EPR, ENDOR, and DFT Studies of Doublet and Triplet Open-Shell Systems
620(1)
7.8.1.1 Introduction
621(5)
7.8.1.2 Experimental
626(2)
7.8.1.3 Theoretical
628(1)
7.8.1.4 Results and Discussion
629(11)
7.9 Cyclotides as Example of Cyclic Proteins with Trefoil Knot and Mobius Strip Topology
640(31)
7.9.1 More about Knot Topology of Lines in Relation to Mobius Strip Topology of Surfaces
647(4)
7.9.2 Cyclotides in Medical Therapy Applications
651(2)
7.9.3 Oral Activity of a Nature-Derived Cyclic Peptide for the Treatment of Multiple Sclerosis
653(18)
8 The Mobius Strip Topology: Applications from Physics and Nanomaterials
671(46)
8.1 Quantization of the Hall Effect
678(7)
8.2 A Primer on Topological Insulators
685(5)
8.3 Graphene-Based Topological Insulators
690(5)
8.4 Spin States of Mobius Graphene Nanoribbons
695(4)
8.5 Designing Topological Insulators from Graphene Nanoribbons
699(8)
8.6 Laser Pulses Create Topological State in Graphene
707(10)
9 Mobius Strip Topology: Highlights from the Arts and Architecture
717(154)
9.1 Mobius Strips before Mobius: By the Example of Baroque Music
719(7)
9.2 Pre-M6bius One-Sidedness: By the Example of Visual Arts and Architecture
726(2)
9.3 More Twisted Bands from Roman Mosaics, the Ouroboros and Infinity
728(3)
9.4 Mathematics and Architecture, Symmetry and Beauty in the Arts and Sciences
731(33)
9.4.1 Influence of Mathematics on Art and Architecture over the Centuries
732(1)
9.4.2 Symmetry and Beauty
733(14)
9.4.2.1 Interplay of Aesthetics and Science
747(3)
9.4.2.2 Symmetry and Architecture
750(6)
9.4.2.3 Symmetry and Poetry
756(8)
9.5 Mobius Strip Topology in Literature, Theater, and Film
764(33)
9.5.1 "La Banda de Moebius" Theater Play by Antonio Toga, Neza (Mexico City), 2020
766(3)
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
769(4)
9.5.3 "The Bald Soprano," Theater Play by Eugene Ionesco, 1950
773(4)
9.5.4 "Kata-Omoi" ("One-Sided Love"), Mystery Novel by Keigo Higashino, 2001
777(5)
9.5.5 "A Subway Named Mobius," Short Story by Armin Joseph Deutsch, 1950, and "Moebius," a Film by Gustavo Daniel Mosquera R, 1996
782(13)
9.5.6 "Mobius," Film by Eric Rochant, 2013
795(2)
9.6 Mobius Topology in Sculpture
797(15)
9.6.1 Max Bill (1908-94), Switzerland
797(5)
9.6.2 Keizo Ushio (Born 1951), Japan
802(5)
9.6.3 Robert R. Wilson (1914-2000), the United States
807(5)
9.7 Mobius Strip Topology: Highlights from Modern Architecture
812(59)
9.7.1 A Fundamental Problem of Architecture when Designing Buildings in Three-Dimensional Space with Several Floors Interconnected by a Mobius Strip Surface
818(5)
9.7.2 Max Reinhardt Haus in Berlin by Peter Eisenman (1992)
823(21)
9.7.3 Mobius House at Het Gooi Near Amsterdam by Ben van Berkel, 1993
844(7)
9.7.4 Phoenix International Media Center in Beijing by Shao Weiping, 2004
851(11)
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
862(9)
Index 871
Klaus Möbius received his Diploma in physics and chemistry (1962), his PhD in natural sciences (1965), and his Habilitation in experimental physics (1969) from the Free University Berlin (FUB), Germany. After his postdoctoral research at the University of California, USA, he joined FUB as a professor (1971). His magnetic resonance research on (bio)organic molecules was driven by national and international collaborations, for example, with groups in Berlin, Munich, Osnabrück, Mülheim (Ruhr), Jerusalem, Novosibirsk, Kazan, Moscow, Sendai, Leiden, Wroclaw, Padova, and Bologna. He has received numerous honors and awards, such as the Max Planck Research Award (1992); Roessler Lecturer Award, Cornell University, New York (2001); Cross of Merit of the Federal Republic of Germany (2006); invited scholar at Tohoku University, Sendai, Japan (2001); and fellow of the Institute for Advanced Studies at the Universities of Jerusalem (1990) and Bologna (2010).

Martin Plato received his Diploma in physics and mathematics (1962) and his PhD in natural sciences (1965) from FUB. In 1963, he joined the Research Institute of AEG, Germany, and soon became the head of its Scientific Application Laboratory. In 1971, he moved to the Institute of Experimental Physics of FUB as a senior scientist in the research group of Prof. Möbius. His main activity there was quantum computational work on super-computers for analyzing magnetic resonance spectra and to determine transient molecular intermediates of bioorganic photoreactions (until his retirement in 1997). He continued the magnetic resonance cooperation with Prof. Möbius at FUB until 2020. Since 2014, he has been working with a research team at Wilhelm Foerster Observatory, Berlin, on astrometric problems such as flyby anomaly of solar space vehicles.

Anton Savitsky received his Diploma in physics (1993) from Novosibirsk University, Russia, and his PhD (1996) from the University of Zurich, Switzerland. In 1997, he joined the research group of Prof. Möbius as a senior researcher. In 2009, he joined the Max Planck Institute of Bioinorganic Chemistry, Mülheim, Germany, as a research group leader. In 2018, he moved to the Department of Physics at the Technical University Dortmund, Germany. His research focuses on developing magnetic resonance methods, in particular at high magnetic fields, and their applications in biology, chemistry, medicine, and physics.