LEADER 03908nam 22007815 450 001 9910983071003321 005 20251030152524.0 010 $a9783031722813 010 $a3031722817 024 7 $a10.1007/978-3-031-72281-3 035 $a(MiAaPQ)EBC31900242 035 $a(Au-PeEL)EBL31900242 035 $a(CKB)37491475200041 035 $a(DE-He213)978-3-031-72281-3 035 $a(OCoLC)1499719717 035 $a(EXLCZ)9937491475200041 100 $a20250207d2025 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGeometry by Its Transformations $eLessons Centered on the History from 1800-1855 /$fby Christopher Baltus 205 $a1st ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Birkhäuser,$d2025. 215 $a1 online resource (297 pages) 225 1 $aCompact Textbooks in Mathematics,$x2296-455X 311 08$a9783031722806 311 08$a3031722809 327 $aIntroduction -- 1. Greek Background -- 2. The Dilation Transformation -- 3. Institutional Transformation of Geometry: France -- 4. Affinity and the List of Transformations by Moebius -- 5. Background for Homology: the Common Secant, the Cross-Ratio, and Harmonic Sets -- 6. Plane-to-Plane Projection -- 7. Homology as developed by La Hire and Poncelet -- 8. Matrices and Homogeneous Coordinates -- 9. Projective Geometry: Steiner and von Staudt -- 10. Transformation in German Universities -- 11. Geometric Inversion -- 12. Moebius Transformation -- 13. Topic after 1855: Beltrami-Klein Model -- 14. Topic after 1855: Isometries and Dilations in French Schoolbooks. 330 $aThis textbook combines the history of synthetic geometry, centered on the years 1800-1855, with a theorem-proof exposition of the geometry developed in those years. The book starts with the background needed from Euclid?s Elements, followed by chapters on transformations, including dilation (similitude), homology, homogeneous coordinates, projective geometry, inversion, the Möbius transformation, and transformation geometry as in French schoolbooks of 1910. Projective geometry is presented by tracing its path through the work of J. V. Poncelet, J. Steiner, and K. G. C. von Staudt. Extensive exercises are included, many from the period studied. The prerequisites for approaching this course are knowledge of high school geometry and enthusiasm for mathematical demonstration. This textbook is ideal for a college geometry course, for self-study, or as preparation for the study of modern geometry. 410 0$aCompact Textbooks in Mathematics,$x2296-455X 606 $aMathematics 606 $aHistory 606 $aGeometry, Projective 606 $aSocial sciences 606 $aGeometry 606 $aHistory of Mathematical Sciences 606 $aProjective Geometry 606 $aMathematics in the Humanities and Social Sciences 606 $aGeometry 606 $aMatemàtica$2thub 606 $aHistòria$2Thub 606 $aGeometria projectiva$2thub 606 $aCiències socials$2thub 608 $aLlibres electrònics$2thub 615 0$aMathematics. 615 0$aHistory. 615 0$aGeometry, Projective. 615 0$aSocial sciences. 615 0$aGeometry. 615 14$aHistory of Mathematical Sciences. 615 24$aProjective Geometry. 615 24$aMathematics in the Humanities and Social Sciences. 615 24$aGeometry. 615 7$aMatemàtica. 615 7$aHistòria 615 7$aGeometria projectiva 615 7$aCiències socials 676 $a510.9 700 $aBaltus$b Christopher$0879371 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910983071003321 996 $aGeometry by Its Transformations$94317354 997 $aUNINA