LEADER 03417nam 2200553 450 001 9910659479103321 005 20240116134718.0 010 $a3-031-23525-8 024 7 $a10.1007/978-3-031-23525-2 035 $a(MiAaPQ)EBC7204900 035 $a(Au-PeEL)EBL7204900 035 $a(CKB)26162320800041 035 $a(DE-He213)978-3-031-23525-2 035 $a(PPN)268210098 035 $a(EXLCZ)9926162320800041 100 $a20230517d2023 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 12$aA Full Axiomatic Development of High School Geometry /$fDavid M. Clark and Samrat Pathania 205 $a1st ed. 2023. 210 1$aCham, Switzerland :$cSpringer Nature Switzerland AG,$d[2023] 210 4$d©2023 215 $a1 online resource (140 pages) 311 08$aPrint version: Clark, David M. A Full Axiomatic Development of High School Geometry Cham : Springer International Publishing AG,c2023 9783031235245 320 $aIncludes bibliographical references and index. 327 $aFoundational Principles -- Neutral Geometry -- Similar Figures -- Area Measure -- Angle Measure -- Trigonometry -- Circle Measure -- Consistency and Models -- Appendix A: Axioms -- Appendix B: MCL #9 -- Appendix C: Font Guide -- Appendix D: Theorem Index -- Appendix E: Notation Index -- Bibliography -- Index. . 330 $aThis textbook provides a full and complete axiomatic development of exactly that part of plane Euclidean geometry that forms the standard content of high school geometry. It begins with a set of points, a measure of distance between pairs of points and ten simple axioms. From there the notions of length, area and angle measure, along with congruence and similarity, are carefully defined and their properties proven as theorems. It concludes with a proof of the consistency of the axioms used and a full description of their models. It is provided in guided inquiry (inquiry-based) format with the intention that students will be active learners, proving the theorems and presenting their proofs to their class with the instructor as a mentor and a guide. The book is written for graduate and advanced undergraduate students interested in teaching secondary school mathematics, for pure math majors interested in learning about the foundations of geometry, for faculty preparing future secondary school teachers and as a reference for any professional mathematician. It is written with the hope of anchoring K-12 geometry in solid modern mathematics, thereby fortifying the teaching of secondary and tertiary geometry with a deep understanding of the subject. 606 $aGeometry$xStudy and teaching (Secondary) 606 $aGeometry, Projective$xFoundations. 606 $aGeometria$2thub 606 $aEducació secundària$2thub 608 $aLlibres electrònics$2thub 615 0$aGeometry$xStudy and teaching (Secondary) 615 0$aGeometry, Projective$xFoundations. . 615 7$aGeometria 615 7$aEducació secundària 676 $a516 700 $aClark$b David M.$f1947-$01359229 702 $aPathania$b Samrat 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910659479103321 996 $aA Full Axiomatic Development of High School Geometry$93373220 997 $aUNINA