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Main Authors:	Specht, Edward John 1915-2011 (Author), Jones, Harold Trainer 1925-1995 (Author), Calkins, Keith G. 1958- (Author), Rhoads, Donald (Author)
Format:	Electronic eBook
Language:	English
Published:	[Basel] Birkhäuser [2015]
Subjects:	Mathematics Geometry History History of Mathematical Sciences Geschichte Mathematik Euklidische Geometrie
Links:	https://doi.org/10.1007/978-3-319-23775-6 https://doi.org/10.1007/978-3-319-23775-6 https://doi.org/10.1007/978-3-319-23775-6 https://doi.org/10.1007/978-3-319-23775-6 https://doi.org/10.1007/978-3-319-23775-6 https://doi.org/10.1007/978-3-319-23775-6 https://doi.org/10.1007/978-3-319-23775-6 https://doi.org/10.1007/978-3-319-23775-6 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028730164&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028730164&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA
Physical Description:	1 Online Ressource (XIX, 527 Seiten, 59 illus)
ISBN:	9783319237756
DOI:	10.1007/978-3-319-23775-6

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Record in the Search Index

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adam_text	EUCLIDEAN GEOMETRY AND ITS SUBGEOMETRIES / SPECHT, EDWARD JOHN : 2015 TABLE OF CONTENTS / INHALTSVERZEICHNIS PREFACE PRELIMINARIES AND INCIDENCE GEOMETRY (I) AFFINE GEOMETRY: INCIDENCE WITH PARALLELISM (IP) COLLINEATIONS OF AN AFFINE PLANE (CAP) INCIDENCE AND BETWEENNESS (IB) PASCH GEOMETRY (PSH) ORDERING A LINE IN THE PASCH PLANE (ORD) COLLINEATIONS PRESERVING BETWEENNESS (COBE) NEUTRAL GEOMETRY (NEUT) FREE SEGMENTS OF A NEUTRAL PLANE (FSEG) ROTATIONS ABOUT A POINT OF A NEUTRAL PLANE (ROT) EUCLIDEAN GEOMETRY BASICS (EUC) ISOMETRIES OF A EUCLIDEAN PLANE (ISM) DILATIONS OF A EUCLIDEAN PLANE (DLN) EVERY LINE IN A EUCLIDEAN PLANE IS AN ORDERED FIELD (OF) SIMILARITY ON A EUCLIDEAN PLANE (SIM) AXIAL AFFINITIES OF A EUCLIDEAN PLANE (AX) RATIONAL POINTS ON A LINE (QX).-A LINE AS REAL NUMBERS (REAL); COORDINATIZATION OFA PLANE (RR) BELINEATIONS ON A EUCLIDEAN/LUB PLANE (AA) RATIOS OF SENSED SEGMENTS (RS) CONSISTENCY AND INDEPENDENCE OF AXIOMS; OTHER MATTERS INVOLVING MODELS REFERENCES INDEX DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT. EUCLIDEAN GEOMETRY AND ITS SUBGEOMETRIES / SPECHT, EDWARD JOHN : 2015 ABSTRACT / INHALTSTEXT IN THIS MONOGRAPH, THE AUTHORS PRESENT A MODERN DEVELOPMENT OF EUCLIDEAN GEOMETRY FROM INDEPENDENT AXIOMS, USING UP-TO-DATE LANGUAGE AND PROVIDING DETAILED PROOFS. THE AXIOMS FOR INCIDENCE, BETWEENNESS, AND PLANE SEPARATION ARE CLOSE TO THOSE OF HILBERT. THIS IS THE ONLY AXIOMATIC TREATMENT OF EUCLIDEAN GEOMETRY THAT USES AXIOMS NOT INVOLVING METRIC NOTIONS AND THAT EXPLORES CONGRUENCE AND ISOMETRIES BY MEANS OF REFLECTION MAPPINGS. THE AUTHORS PRESENT THIRTEEN AXIOMS IN SEQUENCE, PROVING AS MANY THEOREMS AS POSSIBLE AT EACH STAGE AND, IN THE PROCESS, BUILDING UP SUBGEOMETRIES, MOST NOTABLY THE PASCH AND NEUTRAL GEOMETRIES. STANDARD TOPICS SUCH AS THE CONGRUENCE THEOREMS FOR TRIANGLES, EMBEDDING THE REAL NUMBERS IN A LINE, AND COORDINATIZATION OF THE PLANE ARE INCLUDED, AS WELL AS THEOREMS OF PYTHAGORAS, DESARGUES, PAPPAS, MENELAUS, AND CEVA. THE FINAL CHAPTER COVERS CONSISTENCY AND INDEPENDENCE OF AXIOMS, AS WELL AS INDEPENDENCE OF DEFINITION PROPERTIES. THERE ARE OVER 300 EXERCISES; SOLUTIONS TO MANY OF THESE, INCLUDING ALL THAT ARE NEEDED FOR THIS DEVELOPMENT, ARE AVAILABLE ONLINE AT THE HOMEPAGE FOR THE BOOK AT WWW.SPRINGER.COM. SUPPLEMENTARY MATERIAL IS AVAILABLE ONLINE COVERING CONSTRUCTION OF COMPLEX NUMBERS, ARC LENGTH, THE CIRCULAR FUNCTIONS, ANGLE MEASURE, AND THE POLYGONAL FORM OF THE JORDAN CURVE THEOREM. EUCLIDEAN GEOMETRY AND ITS SUBGEOMETRIES IS INTENDED FOR ADVANCED STUDENTS AND MATURE MATHEMATICIANS, BUT THE PROOFS ARE THOROUGHLY WORKED OUT TO MAKE IT ACCESSIBLE TO UNDERGRADUATE STUDENTS AS WELL. IT CAN BE REGARDED AS A COMPLETION, UPDATING, AND EXPANSION OF HILBERT S WORK, FILLING A GAP IN THE EXISTING LITERATURE DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
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author	Specht, Edward John 1915-2011 Jones, Harold Trainer 1925-1995 Calkins, Keith G. 1958- Rhoads, Donald
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isbn	9783319237756
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spellingShingle	Specht, Edward John 1915-2011 Jones, Harold Trainer 1925-1995 Calkins, Keith G. 1958- Rhoads, Donald Euclidean geometry and its subgeometries Mathematics Geometry History History of Mathematical Sciences Geschichte Mathematik Euklidische Geometrie (DE-588)4137555-5 gnd
subject_GND	(DE-588)4137555-5
title	Euclidean geometry and its subgeometries
title_auth	Euclidean geometry and its subgeometries
title_exact_search	Euclidean geometry and its subgeometries
title_full	Euclidean geometry and its subgeometries Edward John Specht (1915–2011), Harold Trainer Jones (1925–1995), Keith G. Calkins, Donald H. Rhoads
title_fullStr	Euclidean geometry and its subgeometries Edward John Specht (1915–2011), Harold Trainer Jones (1925–1995), Keith G. Calkins, Donald H. Rhoads
title_full_unstemmed	Euclidean geometry and its subgeometries Edward John Specht (1915–2011), Harold Trainer Jones (1925–1995), Keith G. Calkins, Donald H. Rhoads
title_short	Euclidean geometry and its subgeometries
title_sort	euclidean geometry and its subgeometries
topic	Mathematics Geometry History History of Mathematical Sciences Geschichte Mathematik Euklidische Geometrie (DE-588)4137555-5 gnd
topic_facet	Mathematics Geometry History History of Mathematical Sciences Geschichte Mathematik Euklidische Geometrie
url	https://doi.org/10.1007/978-3-319-23775-6 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028730164&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028730164&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA
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