The Theory of Plane Area at the Crossroads - Giovannini, Eduardo N.; Haeusler, Edward Hermann; Lassalle Casanave, Abel; - Prospero Internet Bookshop

The Theory of Plane Area at the Crossroads: Philosophical, Historical, and Logical Perspectives
 
Product details:

ISBN13:9783031709159
ISBN10:3031709152
Binding:Hardback
No. of pages:142 pages
Size:235x155 mm
Language:English
Illustrations: 73 Illustrations, black & white; 5 Illustrations, color
684
Category:

The Theory of Plane Area at the Crossroads

Philosophical, Historical, and Logical Perspectives
 
Edition number: 2024
Publisher: Springer
Date of Publication:
Number of Volumes: 1 pieces, Book
 
Normal price:

Publisher's listprice:
EUR 128.39
Estimated price in HUF:
54 463 HUF (51 869 HUF + 5% VAT)
Why estimated?
 
Your price:

50 105 (47 719 HUF + 5% VAT )
discount is: 8% (approx 4 357 HUF off)
The discount is only available for 'Alert of Favourite Topics' newsletter recipients.
Click here to subscribe.
 
Availability:

Estimated delivery time: In stock at the publisher, but not at Prospero's office. Delivery time approx. 3-5 weeks.
Not in stock at Prospero.
Can't you provide more accurate information?
 
  Piece(s)

 
Short description:

This book explores a cluster of philosophical, historical, and logical problems concerning the foundations of the theory of plane area in elementary geometry. The motivation of this study is a notable geometrical proposition known as De Zolt?s postulate, which asserts that a polygon cannot be equal in area to a proper polygonal part. The book is the first systematic investigation of the philosophical and foundational significance of this proposition, which can also be described as the ?fundamental theorem? of the theory of plane area.



This volume provides a comparative study of Euclid?s development of the theory of area in the Elements and its modern reinterpretation in Hilbert?s classical monograph Foundations of Geometry. It connects the historical reflections on De Zolt?s postulate with the nineteenth-century program of providing a purely geometrical foundation for Euclidean geometry, uncovering a rich array of intertwined conceptual problems. It also shifts the perspective and provides a logical analysis of this geometrical postulate within an original development of the abstract theory of magnitudes, called compatible magnitudes. Finally, it extends the previous formal treatment of De Zolt?s postulate to the case of three-dimensional geometry by producing a type system for polyhedral geometrical mereology. The innovative combination of philosophical, historical, and logical perspectives results in a novel discussion of a fascinating problem at the crossroads of (late) nineteenth-century geometry.  This volume will interest readers in the fields of history and philosophy of mathematics, logic, and formal philosophy.

Long description:

This book explores a cluster of philosophical, historical, and logical problems concerning the foundations of the theory of plane area in elementary geometry. The motivation of this study is a notable geometrical proposition known as De Zolt?s postulate, which asserts that a polygon cannot be equal in area to a proper polygonal part. The book is the first systematic investigation of the philosophical and foundational significance of this proposition, which can also be described as the ?fundamental theorem? of the theory of plane area.



This volume provides a comparative study of Euclid?s development of the theory of area in the Elements and its modern reinterpretation in Hilbert?s classical monograph Foundations of Geometry. It connects the historical reflections on De Zolt?s postulate with the nineteenth-century program of providing a purely geometrical foundation for Euclidean geometry, uncovering a rich array of intertwined conceptual problems. It also shifts the perspective and provides a logical analysis of this geometrical postulate within an original development of the abstract theory of magnitudes, called compatible magnitudes. Finally, it extends the previous formal treatment of De Zolt?s postulate to the case of three-dimensional geometry by producing a type system for polyhedral geometrical mereology. The innovative combination of philosophical, historical, and logical perspectives results in a novel discussion of a fascinating problem at the crossroads of (late) nineteenth-century geometry.  This volume will interest readers in the fields of history and philosophy of mathematics, logic, and formal philosophy.

Table of Contents:

Chapter 1. From Euclidean to Hilbertean Practice: The Theory of Plane Area.- Chapter 2. De Zolt's Postulate: The Geometrical Path.- Chapter 3. De Zolt's Postulate: The Abstract Approach.- Chapter 4. De Zolt's Postulate in Three-Dimensions.