Jesper Lutzen (Department of Mathematical Sciences University of Co

A History of Mathematical Impossibility

• Gebundenes Buch

Produktbeschreibung

This book tells the history of impossibility theorems starting with the ancient Greek proof of the incommensurability of the side and the diagonal in a square.

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Produktdetails

• Verlag: Oxford University Press
• Seitenzahl: 304
• Erscheinungstermin: 26. Januar 2023
• Englisch
• Abmessung: 236mm x 157mm x 25mm
• Gewicht: 658g
• ISBN-13: 9780192867391
• ISBN-10: 0192867393
• Artikelnr.: 65771201

Autorenporträt

Jesper Lützen is a historian of mathematics and the physical sciences. He is Professor Emeritus at the Department of Mathematical Sciences at the University of Copenhagen, where he has taught since 1989.

Inhaltsangabe

* 1: Introduction
* 2: Prehistory: Recorded and Non-Recorded Impossibilities
* 3: The First Impossibility Proof: Incommensurability
* 4: The Classical Problems in Antiquity: Constructions and Positive
Theorems
* 5: The Classical Problems: The Impossibility Question
* 6: Diorisms and Conclusions about the Greeks and the Medieval Arabs
* 7: Cube Duplication and Angle Trisection in the 17th and 18th
Centuries
* 8: Circle Quadrature in the 17th Century
* 9: Circle Quadrature in the 18th Century
* 10: Impossible Equations Made Possible: The Complex Numbers
* 11: Euler and the Bridges of Königsberg
* 12: The Insolvability of the Quintic by Radicals
* 13: Constructions with Ruler and Compass: The Final Impossibility
Proofs
* 14: Impossible Integrals
* 15: Impossibility of Proving the Parallel Postulate
* 16: Hilbert and Impossible Problems
* 17: Hilbert and Gödel on Axiomatization and Incompleteness
* 18: Fermat's Last Theorem
* 19: Impossibility in Physics
* 20: Arrow's Impossibility Theorem
* 21: Conclusion