Math shortcuts, Articles, worksheets, Exam tips, Question, Answers, FSc, BSc, MSc
0. Introduction 1. Preliminaries Part-I Euclidean geometry 2. The Axioms 3. Half-planes 4. Congruent triangles 5. Perpendicular lines 6. Similar triangles 7. Parallel lines 8. Triangle geometry Part-II Inversive geometry 9. Inscribed angles 10. Inversion Part-III Non-Euclidean geometry 11. Neutral Geometry 12. Hyperbolic plane 13. Geometry of h-plane Part-IV Additional topics 14. Affine geometry 15. Projective geometry 16. Spherical geometry 17. Projective model 18. Complex coordinates 19. Geometric constructions 20. Area
Euclidean Plane and Its Relatives by Anton Petrunin is a rigorous yet accessible open textbook designed to bridge elementary geometry with advanced metric space theory. Unlike traditional introductory treatments, Petrunin frames plane geometry through distance functions and geometric transformations. This intuitive approach provides undergraduate mathematics majors with a clear foundation in modern axiomatic plane geometry and comparative space structures. The curriculum systematically moves from standard Euclidean axioms to hyperbolic and spherical geometries, illustrating how fundamental principles adapt across non-Euclidean surfaces. By integrating concrete geometric exercises with formal proof construction, Petrunin eliminates abstract ambiguity, enabling independent scholars to analyze complex spatial relationships and execute precise non-Euclidean geometric proofs with total analytical confidence. Widely commended for its concise clarity and pedagogical precision, this modern mathematical work serves as an outstanding reference for university courses and self-study. Petrunin’s modern structural framework equips aspiring mathematicians with classical synthetic metric space solutions, building the foundational logic necessary for graduate-level topology and differential geometry.
Title: Euclidean Plane and Its Relatives by Anton Petrunin Publisher: arXiv Year: 2017 Pages: 198 Type: PDF Language: English ISBN-10 #: 1650229674 ISBN-13 #: 978-1650229676 License: CC BY-SA 4.0 Amazon: Amazon
The author Anton Petrunin is a prominent Russian-American mathematician and professor of mathematics at Pennsylvania State University. Specializing in metric geometry, Alexandrov spaces, and differential geometry, Petrunin is widely recognized for making complex geometric concepts intuitive for university students and researchers worldwide. Beyond his university research, he actively advocates for open-access mathematical literature and educational equity. His open textbook contributions remain influential benchmarks for modern educators developing twenty-first century university geometry pedagogy and open learning resources.
Join with us :-
© 2025 - 2026 Free Mathematics Books
.