Geometry Through History

Preface.- 1. The Elements of Euclid.- 2. Neutral Geometry.- 3. The Hyperbolic Plane.- 4. Hilbert's Grundlagen .- 5. More Euclidean Geometry.- 6. Models for the Hyperbolic Plane.- 7. Affine Geometry.- 8. An Introduction to Projective Geometry.- 9. Algebraic Curves.- 10. Rotations and Quaternions.- Index.

Meighan Dillon is a Professor of Mathematics at Kennesaw State University. She is a life-long educator, whose research in infinite-dimensional Lie algebras is complemented by explorations in pedagogy and the use of projective geometry in art.

"While the book covers some advanced topics, it is also remarkably accessible: anyone with a year of college-level mathematics and a love of geometry will find value in this text, as Dillon (Kennesaw State Univ.) explores axioms, proofs, and an array of fascinating problems. ... One of the most appealing aspects of this book is the author's way of introducing projective geometry to pique the reader's interest in modern algebra. ... Summing Up: Recommended. Lower-division undergraduates and above." (J. A. Bakal, Choice, Vol. 56 (03), November, 2018)

"It discusses a lot of interesting topics in geometry, it is clearly written and should be accessible to its target audience of students ... . it offers students an opportunity to see the relationship between geometry and other areas of mathematics, including abstract and linear algebra. If you are teaching a course in geometry at the college level and the topics discussed here are compatible with your course, this book certainly merits a serious look." (Mark Hunacek, MAA Reviews, October, 2018)
"This is a wonderful new book that could be used as a textbook for geometry, but would be of interest to any mathematician whose work includes some geometry or who is interested in the history of mathematical developments. ... The book offers a deep, thorough, and entertaining presentation of geometry through history." (Tara D. Taylor, Mathematical Reviews, January, 2019)