Worlds Out of Nothing

DOI10.1007/978-1-84628-633-9zbMath1111.01005OpenAlexW4206413076MaRDI QIDQ3413666

Publication date: 14 December 2006

Published in: Springer Undergraduate Mathematics Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-1-84628-633-9

zbMATH Keywords

duality non-Euclidean geometry projective geometry Poincaré Möbius Plücker Poncelet

Mathematics Subject Classification ID

History of mathematics in the 20th century (01A60) History of algebraic geometry (14-03) History of differential geometry (53-03) History of mathematics in the 19th century (01A55) General theory of linear incidence geometry and projective geometries (51A05) Research exposition (monographs, survey articles) pertaining to history and biography (01-02) History of relativity and gravitational theory (83-03) Möbius geometries (51B10) General histories, source books (01A05) History of geometry (51-03) Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations) (51M35)

Related Items (21)

Reviews ⋮ PROJECTIVE DUALITY AND THE RISE OF MODERN LOGIC ⋮ Brianchon and Poncelet's joint memoir, the nine-point circle, and beyond ⋮ On mathematical towers of Babel and ``translation as an epistemic category ⋮ Charles Peirce and Bertrand Russell on Euclid ⋮ Book review of: B. Riemann, Über die Hypothesen, welche der Geometrie zu Grunde liegen; D. Hilbert, Grundlagen der Geometrie (Festschrift 1899) ⋮ Frege on intuition and objecthood in projective geometry ⋮ New series for the cosine lemniscate function and the polynomialization of the lemniscate integral ⋮ Poncelet's porism: a long story of renewed discoveries. I ⋮ Frege and the origins of model theory in nineteenth century geometry ⋮ What did Gauss read in the appendix? ⋮ von Staudt`s theory of ``Würfe`` (jets) -- an irruption of algebra in pure geometry ⋮ The fundamental theorem of projective geometry: evolution of its proof between 1847 and 1900 ⋮ PASCH’S PHILOSOPHY OF MATHEMATICS ⋮ HILBERT, DUALITY, AND THE GEOMETRICAL ROOTS OF MODEL THEORY ⋮ The principle of duality in Euclidean and in absolute geometry ⋮ The mystery of Riemann's curvature ⋮ Jakob Steiner's \textit{Systematische Entwickelung}: the culmination of classical geometry ⋮ Dynamic hyperbolic geometry: building intuition and understanding mediated by a Euclidean model ⋮ Figures real, imagined, and missing in Poncelet, Plücker, and Gergonne ⋮ Mathematical instruments from times of crisis

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