This book presents the foundations of Euclidean geometry from the point of view of mathematics, taking advantage of all the developments since the appearance of Hilbert's classic work. Here, real affine space is characterized by a small number of axioms involving points and line segments making the treatment self-contained and thorough. This treatment is accessible for final year undergraduates and graduate students, and can also serve as an introduction to other areas of mathematics such as matroids and antimatroids, combinatorial convexity, the theory of polytopes, projective geometry and functional analysis.
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Editorial Reviews
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'Altogether a very interesting booklet which can be recommended already for final year undergraduates.' G. Kowol, Wien, , Book Reviews
'... valuable complement to the large amount of existing literature on 'classical' convexity.' European Mathematical Society
'... valuable complement to the large amount of existing literature on 'classical' convexity.' European Mathematical Society
Book Description
This book on the foundations of Euclidean geometry aims to present the subject from the point of view of present day mathematics, taking advantage of all the devlopments since the appearance of Hilberts classic work. The treatment is self-contained and thorough, many results being established under weaker hypotheses than usual.The book can serve as an introduction to other areas of mathematics such as matroids and antimatroids, combinatorial convexity, the theory of polytopes, projective geometry and functional analysis.
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First Sentence:
This chapter is of a preparatory nature. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
dense linear geometry, affine independent set, affine independent subset, nonempty affine subset, ordered division ring, normed real vector space, intrinsic interior, maximality theorem, distinct collinear points, aligned space, convex partition, nonempty face, affine basis, convex geometry, affine set, hull operator, nonempty convex sets, convex geometries, maximal independent subset, whose vertex set, factor geometries, convex closure, lattice homomorphism, affine hull, coplanar lines Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Proof By Proposition, Proof Suppose, Proof Put, Proof Obviously, Proof Evidently, Proof Assume, Proof Choose New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
This chapter is of a preparatory nature. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
dense linear geometry, affine independent set, affine independent subset, nonempty affine subset, ordered division ring, normed real vector space, intrinsic interior, maximality theorem, distinct collinear points, aligned space, convex partition, nonempty face, affine basis, convex geometry, affine set, hull operator, nonempty convex sets, convex geometries, maximal independent subset, whose vertex set, factor geometries, convex closure, lattice homomorphism, affine hull, coplanar lines Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Proof By Proposition, Proof Suppose, Proof Put, Proof Obviously, Proof Evidently, Proof Assume, Proof Choose New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 9
books:
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12
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- Introduction to the Analysis of Metric Spaces (Australian Mathematical Society Lecture Series) by John R. Giles in Front Matter
- Modelling with Differential and Difference Equations (Australian Mathematical Society Lecture Series) by Glenn Fulford in Front Matter
- Geometric Analysis and Lie Theory in Mathematics and Physics (Australian Mathematical Society Lecture Series) by Alan L. Carey in Front Matter
- Nicht-Euklidische Geometrie by Felix Klein in Back Matter
- The Mathematics of Projectiles in Sport (Australian Mathematical Society Lecture Series) by Neville de Mestre in Front Matter
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- Introduction to the Analysis of Normed Linear Spaces (Australian Mathematical Society Lecture Series) by J. R. Giles in Front Matter
- Convex Polytopes (Graduate Texts in Mathematics) (v. 221) by Branko Grünbaum in Back Matter
- Geometric Approaches to Differential Equations (Australian Mathematical Society Lecture Series) by Peter J. Vassiliou in Front Matter
- Industrial Mathematics: Case Studies in the Diffusion of Heat and Matter (Australian Mathematical Society Lecture Series) by Glenn R. Fulford in Front Matter
- Modern Projective Geometry (Mathematics And Its Applications Volume 521) (Mathematics and Its Applications (closed)) by Claude-Alain Faure in Back Matter
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