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Eine Geschichte der mathematischen Unmöglichkeit von Jesper Lützen: Neu
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eBay-Artikelnr.:404266706746
Artikelmerkmale
- Artikelzustand
- Book Title
- A History of Mathematical Impossibility
- Publication Date
- 2023-01-26
- ISBN
- 9780192867391
Über dieses Produkt
Product Identifiers
Publisher
Oxford University Press, Incorporated
ISBN-10
0192867393
ISBN-13
9780192867391
eBay Product ID (ePID)
21058368840
Product Key Features
Number of Pages
298 Pages
Publication Name
History of Mathematical Impossibility
Language
English
Publication Year
2023
Subject
General
Type
Textbook
Subject Area
Mathematics
Format
Hardcover
Dimensions
Item Height
0.8 in
Item Weight
23.4 Oz
Item Length
9.4 in
Item Width
6.4 in
Additional Product Features
Intended Audience
Scholarly & Professional
LCCN
2022-942881
TitleLeading
A
Dewey Edition
23
Reviews
"This book is intended as a semi-popular volume: in it, the author eschews mathematical or historical technicalities, instead providing succinct yet rich accounts that neatly convey the main conceptual innovations and transformations at the heart of the episodes discussed therein...The writing is clear and engaging." -- Historia Mathematica, This book is intended as a semi-popular volume: in it, the author eschews mathematical or historical technicalities, instead providing succinct yet rich accounts that neatly convey the main conceptual innovations and transformations at the heart of the episodes discussed therein...The writing is clear and engaging.
Illustrated
Yes
Dewey Decimal
515.09
Table Of Content
1. Introduction2. Prehistory: Recorded and Non-Recorded Impossibilities3. The First Impossibility Proof: Incommensurability4. The Classical Problems in Antiquity: Constructions and Positive Theorems5. The Classical Problems: The Impossibility Question6. Diorisms and Conclusions about the Greeks and the Medieval Arabs7. Cube Duplication and Angle Trisection in the 17th and 18th Centuries8. Circle Quadrature in the 17th Century9. Circle Quadrature in the 18th Century10. Impossible Equations Made Possible: The Complex Numbers11. Euler and the Bridges of Königsberg12. The Insolvability of the Quintic by Radicals13. Constructions with Ruler and Compass: The Final Impossibility Proofs14. Impossible Integrals15. Impossibility of Proving the Parallel Postulate16. Hilbert and Impossible Problems17. Hilbert and Gödel on Axiomatization and Incompleteness18. Fermat's Last Theorem19. Impossibility in Physics20. Arrow's Impossibility Theorem21. Conclusion
Synopsis
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., Many of the most famous results in mathematics are impossibility theorems stating that something cannot be done. Good examples include the quadrature of the circle by ruler and compass, the solution of the quintic equation by radicals, Fermat's last theorem, and the impossibility of proving the parallel postulate from the other axioms of Euclidean geometry. This book tells the history of these and many other impossibility theorems starting with the ancient Greek proof of the incommensurability of the side and the diagonal in a square. Lützen argues that the role of impossibility results have changed over time. At first, they were considered rather unimportant meta-statements concerning mathematics but gradually they obtained the role of important proper mathematical results that can and should be proved. While mathematical impossibility proofs are more rigorous than impossibility arguments in other areas of life, mathematicians have employed great ingenuity to circumvent impossibilities by changing the rules of the game. For example, complex numbers were invented in order to make impossible equations solvable. In this way, impossibilities have been a strong creative force in the development of mathematics, mathematical physics, and social science.
LC Classification Number
MLCM 2024/44219 (Q)
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AlibrisBooks
98,6% positive Bewertungen•1.9 Mio. Artikel verkauft
Angemeldet als gewerblicher Verkäufer
Verkäuferbewertungen (511'901)
- 0***n (168)- Bewertung vom Käufer.Letzter MonatBestätigter KaufAn item every man needs in his man cave!
- m***d (52)- Bewertung vom Käufer.Letzter MonatBestätigter KaufVery great quality and excellent condition For the value it was purchased at! The appearance of this book is near mint condition.
- w***w (455)- Bewertung vom Käufer.Letzter MonatBestätigter KaufSuper seller in every way!