Geometry: The Line and the Circle
Title | Geometry: The Line and the Circle PDF eBook |
Author | Maureen T. Carroll |
Publisher | American Mathematical Soc. |
Pages | 480 |
Release | 2018-12-20 |
Genre | Geometry |
ISBN | 1470448432 |
Geometry: The Line and the Circle is an undergraduate text with a strong narrative that is written at the appropriate level of rigor for an upper-level survey or axiomatic course in geometry. Starting with Euclid's Elements, the book connects topics in Euclidean and non-Euclidean geometry in an intentional and meaningful way, with historical context. The line and the circle are the principal characters driving the narrative. In every geometry considered—which include spherical, hyperbolic, and taxicab, as well as finite affine and projective geometries—these two objects are analyzed and highlighted. Along the way, the reader contemplates fundamental questions such as: What is a straight line? What does parallel mean? What is distance? What is area? There is a strong focus on axiomatic structures throughout the text. While Euclid is a constant inspiration and the Elements is repeatedly revisited with substantial coverage of Books I, II, III, IV, and VI, non-Euclidean geometries are introduced very early to give the reader perspective on questions of axiomatics. Rounding out the thorough coverage of axiomatics are concluding chapters on transformations and constructibility. The book is compulsively readable with great attention paid to the historical narrative and hundreds of attractive problems.
The Circle
Title | The Circle PDF eBook |
Author | Alfred S. Posamentier |
Publisher | Prometheus Books |
Pages | 352 |
Release | 2016-08-23 |
Genre | Mathematics |
ISBN | 1633881687 |
The circle has fascinated mathematicians since ancient times. This entertaining book describes in layperson’s terms the many intriguing properties of this fundamental shape. If math has intimidated you, this may be the ideal book to help you appreciate the discipline through one of its most important elements. The authors begin with a brief review of the basic properties of the circle and related figures. They then show the many ways in which the circle manifests itself in the field of geometry—leading to some amazing relationships and truly important geometric theorems. In addition, they explore remarkable circle constructions and demonstrate how all constructions in geometry that usually require an unmarked straightedge and a compass can also be done with the compass alone. Among other things, the reader will learn that circles can generate some unusual curves – many even quite artistic. Finally, the role of circles in art and architecture and a discussion of the circle’s place on the sphere bring "full circle" this presentation of a key element of geometry.
The Circle and Straight Line
Title | The Circle and Straight Line PDF eBook |
Author | John Harris |
Publisher | |
Pages | 250 |
Release | 1875 |
Genre | Circle-squaring |
ISBN |
The Right Line & Circle (coordinate Geometry)
Title | The Right Line & Circle (coordinate Geometry) PDF eBook |
Author | William Briggs |
Publisher | |
Pages | 268 |
Release | 1908 |
Genre | Coordinates |
ISBN |
Analytical Geometry (the Straight Line and Circle).
Title | Analytical Geometry (the Straight Line and Circle). PDF eBook |
Author | Arthur Le Sueur |
Publisher | |
Pages | 120 |
Release | 1886 |
Genre | Circle |
ISBN |
A Treatise on the Circle and the Sphere
Title | A Treatise on the Circle and the Sphere PDF eBook |
Author | Julian Lowell Coolidge |
Publisher | |
Pages | 614 |
Release | 1916 |
Genre | Circle |
ISBN |
The Geometry of Remarkable Elements
Title | The Geometry of Remarkable Elements PDF eBook |
Author | Constantin Mihalescu |
Publisher | |
Pages | 0 |
Release | 2016 |
Genre | Geometry, Modern |
ISBN | 9780996874519 |
This book is an English translation of a text written by Constantin Mihalescu, a retired artillery colonel and enthusiastic amateur mathematician. With the majority of the results obtained in the second half of the 19th century and the first half of the 20th century, this book was one of the most complete descriptions of geometry of its time. It contains a comprehensive collection of the most important properties of points, lines, and circles related to triangles and quadrilaterals, as they were known by the mid-1950s, and a rich assortment of problems to entice and inspire readers of all levels. Topics covered include the nine-point circle, the Simson line, the orthopolar triangles, the orthopole, the Gergonne and Nagel points, the Miquel point and circle, the Carnot circle, the Brocard points, the Lemoine point and circles, the Newton-Gauss line, and much more.