Apostol, Tom M.; Mnatsakanian, Mamikon A. New horizons in geometry. (English) Zbl 1268.51001 The Dolciani Mathematical Expositions 47. Washington, DC: Mathematical Association of America (MAA) (ISBN 978-0-88385-354-2/hbk; 978-1-61444-210-3/ebook). xiv, 513 p. (2012). Review partially taken from the book’s introduction and foreword.This book is a compendium of joint work produced by the authors during the period 1998–2012, most of it published in American Mathematical Monthly, Math Horizons, Mathematical Magazine, and The Mathematical Gazette. The published papers have been edited, augmented and rearranged into 15 chapters dealing with several parts of classical geometry. The authors provide fresh and powerful insights into geometry that requires only a modest background in mathematics. Using new and intuitively rich methods, they give beautifully illustrated proofs of results and extensions of familiar theorems. Lengths, areas and volumes of curves, surfaces and solids are explored from a visually captivating perspective. Powerful geometric methods are used to solve standard calculus problems. Constructions and mechanical interpretations in the spirit of Archimedes involving centroids and moments are carried to new heights and to higher dimensional spaces. The hundreds of full color illustrations are visually enticing and provide great motivation to read further and savor the wonderful results. This book is a must have for any geometer. Reviewer: Dirk Keppens (Gent) Cited in 4 ReviewsCited in 5 Documents MSC: 51-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to geometry 51M15 Geometric constructions in real or complex geometry 00A35 Methodology of mathematics 00B10 Collections of articles of general interest Keywords:geometry; geometric construction; calculus PDFBibTeX XMLCite \textit{T. M. Apostol} and \textit{M. A. Mnatsakanian}, New horizons in geometry. Washington, DC: Mathematical Association of America (MAA) (2012; Zbl 1268.51001)