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Fundamental Concepts of Geometry
Fundamental Concepts of Geometry demonstrates in a clear and lucid manner the relationships of several types of geometry to one another. This highly regarded work is a superior teaching text, especially valuable in teacher preparation, as well as providing an excellent overview of the foundations and historical evolution of geometrical concepts.
Professor Meserve (University of Vermont) offers students and prospective teachers the broad mathematical perspective gained from an elementary treatment of the fundamental concepts of mathematics. The clearly presented text is written on an undergraduate (or advanced secondary-school) level and includes numerous exercises and a brief bibliography. An indispensable taddition to any math library, this helpful guide will enable the reader to discover the relationships among Euclidean plane geometry and other geometries; obtain a practical understanding of "proof"; view geometry as a logical system based on postulates and undefined elements; and appreciate the historical evolution of geometric concepts.
Professor Meserve (University of Vermont) offers students and prospective teachers the broad mathematical perspective gained from an elementary treatment of the fundamental concepts of mathematics. The clearly presented text is written on an undergraduate (or advanced secondary-school) level and includes numerous exercises and a brief bibliography. An indispensable taddition to any math library, this helpful guide will enable the reader to discover the relationships among Euclidean plane geometry and other geometries; obtain a practical understanding of "proof"; view geometry as a logical system based on postulates and undefined elements; and appreciate the historical evolution of geometric concepts.
- GenresMathematics
445 pages, Kindle Edition
First published May 1, 1983
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July 12, 2024
As stated in the title, the book provides an introduction to fundamental concepts of geometry.
It starts with an axiomatic formulation of projective geometry, defined in terms of its elementary elements, their relationships and a set of postulates.
Increasing the number of postulates, the author shows how it is possible to introduce coordinates and thus analytic projective geometry.
From there, the authors introduces affine and then Euclidean geometry.
This part forma the bulk of the material, with the last two chapters giving a bird-eye view on non-Euclidean plane geometries and topology.
Throughout the discussion, it is emphasized how new geometries can be derived from more general geometries by adding additional assumptions.
The treatment is elementary but rigorous.
Each chapter comes with several exercises, where often important results are left as proofs for the reader.
This fact, together with the fact that there are no solutions, might displease some readers.
I found that most of the exercises could be easily done after having absorbed the content of the previous chapters; however some exercises are considerably more challenging.
The book is also quite old and comes with a number of pictures which might seem to small for a geometry book.
Overall, I found the book a useful reading.
8/10
It starts with an axiomatic formulation of projective geometry, defined in terms of its elementary elements, their relationships and a set of postulates.
Increasing the number of postulates, the author shows how it is possible to introduce coordinates and thus analytic projective geometry.
From there, the authors introduces affine and then Euclidean geometry.
This part forma the bulk of the material, with the last two chapters giving a bird-eye view on non-Euclidean plane geometries and topology.
Throughout the discussion, it is emphasized how new geometries can be derived from more general geometries by adding additional assumptions.
The treatment is elementary but rigorous.
Each chapter comes with several exercises, where often important results are left as proofs for the reader.
This fact, together with the fact that there are no solutions, might displease some readers.
I found that most of the exercises could be easily done after having absorbed the content of the previous chapters; however some exercises are considerably more challenging.
The book is also quite old and comes with a number of pictures which might seem to small for a geometry book.
Overall, I found the book a useful reading.
8/10
Displaying 1 of 1 review