The Resource An axiomatic approach to geometry, Francis Borceux

# An axiomatic approach to geometry, Francis Borceux

Label
An axiomatic approach to geometry
Title
An axiomatic approach to geometry
Statement of responsibility
Francis Borceux
Creator
Author
Subject
Language
eng
Summary
Focusing methodologically on those historical aspects that are relevant to supporting intuition in axiomatic approaches to geometry, the book develops systematic and modern approaches to the three core aspects of axiomatic geometry: Euclidean, non-Euclidean and projective. Historically, axiomatic geometry marks the origin of formalized mathematical activity. It is in this discipline that most historically famous problems can be found, the solutions of which have led to various presently very active domains of research, especially in algebra. The recognition of the coherence of two-by-two contradictory axiomatic systems for geometry (like one single parallel, no parallel at all, several parallels) has led to the emergence of mathematical theories based on an arbitrary system of axioms, an essential feature of contemporary mathematics. This is a fascinating book for all those who teach or study axiomatic geometry, and who are interested in the history of geometry or who want to see a complete proof of one of the famous problems encountered, but not solved, during their studies: circle squaring, duplication of the cube, trisection of the angle, construction of regular polygons, construction of models of non-Euclidean geometries, etc. It also provides hundreds of figures that support intuition. Through 35 centuries of the history of geometry, discover the birth and follow the evolution of those innovative ideas that allowed humankind to develop so many aspects of contemporary mathematics. Understand the various levels of rigor which successively established themselves through the centuries. Be amazed, as mathematicians of the 19th century were, when observing that both an axiom and its contradiction can be chosen as a valid basis for developing a mathematical theory. Pass through the door of this incredible world of axiomatic mathematical theories!
Member of
GW5XE
Dewey number
516
Illustrations
illustrations
Index
no index present
LC call number
QA445
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Geometric trilogy
Series volume
I
Label
An axiomatic approach to geometry, Francis Borceux
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
• net
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
1.The Prehellenic Antiquity -- 2.Some Pioneers of Greek Geometry -- 3.Euclid's Elements -- 4.Some Masters of Greek Geometry -- 5.Post-Hellenic Euclidean Geometry -- 6.Projective Geometry -- 7.Non-Euclidean Geometry -- 8.Hilbert's Axiomatization of the Plane -- Appendices: A.Constructibily -- B.The Three Classical Problems -- C.Regular Polygons
Control code
ocn864878479
Dimensions
unknown
Extent
1 online resource (xv, 399 pages)
File format
unknown
Form of item
online
Isbn
9783319017303
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-319-01730-3
Other physical details
illustrations
Quality assurance targets
unknown
.b31758484
Sound
unknown sound
Specific material designation
remote
System control number
• (OCoLC)864878479
• springer3319017306

#### Library Locations

• Deakin University Library - Geelong Waurn Ponds Campus
75 Pigdons Road, Waurn Ponds, Victoria, 3216, AU
-38.195656 144.304955