Geometric transformations IV: circular transformations. (English)

Anneli Lax new mathematical library44. Washington, DC: Mathematical Association of America (MAA) (ISBN 978-0-88385-648-2/pbk). 296~p. (2009).

Publisherâ€™s description: This book, which concludes a four-part Geometric Transformations series, can be studied independently of Parts I, II, and III. It develops the geometry of transformations of the plane that map circles to circles (conformal or anallagmatic geometry). The notion of inversion, or reflection in a circle, is the key tool employed. The plane geometry of secondary school - figures composed of lines and circles - takes on a new life when it is viewed as the study of properties that are preserved by special groups of transformations. No longer is there a single, universal geometry: different sets of transformations of the plane correspond to intriguing, disparate geometries. Applications include ruler-and-compass constructions and the PoincarÃ© model of hyperbolic geometry. The presentation assumes background only in elementary geometry and trigonometry.