Geometry: Our Cultural Heritage 2nd Edition by Audun Holme (PDF)

Description

This is a revised edition of the ?rst printing which appeared in 2002. The book is based on lectures at the University of Bergen, Norway.Over the years these lectures have covered many different aspects and facets of the wonderful ?eld of geometry. Consequently it has never been possible to give a full and ?nal account of geometry as such, at an undergraduatelevel: A carefully consideredselection has always been necessary. The present book constitutes the main central themes of these selections. One of the groups I am aiming at, is future teachers of mathematics. All too oftenthe textsdealingwith geometrywhichgo intothe syllabusforteacher-students present the material in ways which appear pedantic and formalistic, suppressing the very powerful and dynamic character of this old ?eld, which at the same time so young. Geometry is a ?eld of mathematical insight, research, history and source of artistic inspiration. And not least important, an integral part of our common cultural heritage.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Noticeable weaknesses are the typos and lapses in grammar on virtually every page. Otherwise the history and current state of geometry are nicely presented, and my objections are again to failings I find to pervade recent geometry and mathematics in general.I will focus here on the author’s discussion of foundations of mathematics (pp.170-176) preceding his more detailed presentations. He speaks characteristically of a high level of precision in present-day logic and set theory, yet I see numerous misconceptions.He describes logic in terms of “boolean functions”, by which a statement P is either true or false, and “No other alternatives exist”. This has been contested since Aristotle. A familiar counterexample is in asking “Did the husband stop or not stop beating his wife?” about a husband who never beat her. The concerned Law of Excluded Middle is accordingly restricted.The author in that vein also assigns to a statement P customary “truth-values”, T and F, applied in “truth tables” for composite statements like “P implies Q”. Briefly, that statement is held, e.g., true if P is false and Q is true. Beside this conflict with the common understanding of implication, also phrased as “if P then Q”, the example conflictingly supposes P true in the implication and false in the truth-value.One other failing I might consider in that part of the book is the misunderstanding (by Russell also) and consequent widespread influence of “Russell’s paradox”. It positsTHE SET OF ALL SETS NOT MEMBERS OF THEMSELVES.For instance, the set of all chairs (not itself a chair) qualifies, but not the set of all non-chairs. It is then observed that if the posited set is a member of itself then, since not in the set, it is contradictorily not a member of itself, and if it is not then, since it qualifies, it is.A like paradox has been noted in consideringA MAN WHO AS BARBER IN A VILLAGE SHAVES ALL MEN IN IT NOT SHAVING THEMSELVES.It has been tried to dismiss this, in efforts to view the paradox as a problem in set theory. But the problem is merely an unrelated apparent contradiction.If the barber shaves ALL those not shaving themselves, he cannot be among them, since he would contradictorily shave himself. And if he shaves ONLY those not shaving themselves, he must be among them, since he would otherwise again contradictorily shave himself. Hence he cannot both shave all and only those in question, but either the first or the second.Likewise, the concerned set cannot include both all and only those in question, but either one or the other.

⭐I ordered this book as new, but I have received a used and very dirty book, almost whole the book is covered with large spots something like black coffee or something else. The book corners are struck and damaged.I do not recommend it to you; don’t boy this book at least from this seller! Just look on the pictures.

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