عنوان

Euclidean geometry and its subgeometries

شابک

9783319237749

کد کشور

IR

شماره

10382

زبان متن نوشتاري يا گفتاري و مانند آن

انگلیسی

کشور محل نشر

IR

عنوان اصلي

Euclidean geometry and its subgeometries

نام عام مواد

[Book]

نام نخستين پديدآور

/ Edward John Specht, Harold Trainer Jones, Keith G. Calkins, Donald H. Rhoads.

محل نشرو پخش و غیره

Cham

نام ناشر، پخش کننده و غيره

Springer International Publishing : Imprint: Birkhäuser

تاریخ نشرو بخش و غیره

, 2015.

نام خاص و کميت اثر

(XIX, 527 pages 59 illustrations

متن يادداشت

Language: انگلیسی

متن يادداشت

Print

متن يادداشت

index

متن يادداشت

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.

عنصر شناسه ای

Geometry.

عنصر شناسه ای

Mathematics.

عنصر شناسه ای

History.

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

Specht, Edward John

مستند نام اشخاص تاييد نشده

Jones, Harold Trainer. author.

مستند نام اشخاص تاييد نشده

Calkins, Keith G. author.

کشور

ایران

سازمان

دانشگاه محقق اردبیلی

تاريخ عمليات

20231204

وضعیت فهرست نویسی

old catalog

فرمت انتشار

p

نوع ماده

BL

کد کاربرگه

270410

پیشوند ISBD اعمال شده است

1

سطح دسترسي

a

تكميل شده

Y