Plain Plane Geometry: A Concise Euclidean Geometry Textbook for Pre-University & Olympiad Students by Amol Sasane

Introduction

Geometry is not just a branch of mathematics; it is the language of shapes, spaces, and logical reasoning. For students in India preparing for competitive examinations, mathematics Olympiads, or simply seeking a deeper understanding of Euclidean geometry, Plain Plane Geometry by Amol Sasane offers a refreshing and rigorous yet accessible journey into the world of points, lines, circles, and theorems. Published by the prestigious World Scientific Publishing Company, this hardbound volume is an indispensable companion for high school and pre-university learners who wish to master the fundamentals of plane geometry through an axiomatic but playful approach.

Book Overview

Plain Plane Geometry is a carefully crafted, concise course that covers the essentials of Euclidean plane geometry. The book is designed to serve as a first introduction to the subject, making it ideal for advanced high school students and those in their early undergraduate years. The author, Amol Sasane, avoids excessive formalism while maintaining logical rigor, ensuring that young readers are not intimidated but instead inspired. Each chapter unfolds with clear definitions, vivid colour illustrations, and a wealth of problems that go beyond routine drills. The exercises are crafted to spark curiosity and a sense of mathematical play, encouraging students to appreciate the elegance and beauty of geometric truths.

Key Highlights

• Axiomatic yet accessible: The book builds geometry from first principles but keeps the language and presentation suitable for a younger audience.
• Abundance of colour illustrations: Every theorem and proof is accompanied by rich, full-colour diagrams that make abstract concepts visually intuitive.
• Challenging and playful exercises: Problems are designed to stimulate creative thinking, not just mechanical repetition. Many are ideal for mathematics circles and Olympiad training.
• Complete solutions section: A detailed section with hints and full solutions to all exercises is included at the end, enabling self-study and independent learning.
• Compact and focused: The book covers all core topics without unnecessary digression, making it an efficient resource for exam preparation.

Inside the Book

The content is structured to guide the reader from basic concepts to more advanced results in plane geometry. Early chapters introduce fundamental notions such as points, lines, angles, triangles, and circles. Later sections delve into congruence, similarity, area theorems, and properties of polygons. The author weaves classical results—like those of Euclid, Pythagoras, and Thales—into a coherent narrative. Every new idea is illustrated with colourful diagrams, and each section ends with a set of problems that range from straightforward applications to brain-teasing puzzles. The hints and solutions at the back make the book self-contained, allowing students to verify their reasoning and learn from mistakes.

Key Topics

• Basic geometric objects: points, lines, rays, segments, and angles
• Triangles: congruence, similarity, special lines (medians, altitudes, angle bisectors)
• Circles: chords, arcs, tangents, cyclic quadrilaterals, and power of a point
• Polygons: quadrilaterals, parallelograms, and area relationships
• Classical theorems: Pythagoras, Thales, Ceva, Menelaus, and more
• Geometric constructions and logical proof techniques

Reader Benefits

Students who work through Plain Plane Geometry will develop a strong foundation in logical reasoning and spatial thinking. The book trains the mind to construct clear, step-by-step proofs—a skill invaluable for mathematics Olympiads, JEE, and other competitive exams in India. The playful problems foster an appreciation for the subject, turning geometry from a chore into a delightful puzzle. Moreover, the self-contained nature of the book (with solutions) allows learners to progress at their own pace, making it perfect for both classroom use and independent study. Teachers and mentors will also find the book a rich source of material for geometry circles and enrichment classes.

Learning Outcomes

• Master the fundamental definitions and axioms of plane Euclidean geometry.
• Gain proficiency in constructing rigorous geometric proofs.
• Understand and apply key theorems related to triangles, circles, and polygons.
• Develop problem-solving strategies applicable to Olympiad-level and competitive exam questions.
• Build visual intuition through extensive use of colour diagrams and geometric reasoning.
• Cultivate a sense of mathematical curiosity and the joy of discovery.

Who Should Read

This book is ideal for advanced high school students (Classes 9 to 12) who are serious about mathematics, especially those preparing for national and international Olympiads, JEE Main/Advanced, or other entrance examinations. It is also well-suited for undergraduate students seeking a refresher in geometry, and for teachers who want to enrich their classroom instruction with challenging, non-routine problems. Anyone with a passion for mathematics and a desire to see geometry in a new, vibrant light will find this book a rewarding read.

About the Author

Amol Sasane is a mathematician and educator with extensive experience in teaching and writing at the pre-university and university levels. He has a knack for presenting complex mathematical ideas in an engaging and accessible manner, as evidenced by his several well-received books. His deep understanding of geometry and his commitment to nurturing young mathematical talent shine through in every page of Plain Plane Geometry.

About the Publisher

World Scientific Publishing Company is a leading international academic publisher with a strong reputation for publishing high-quality books in science, mathematics, and engineering. Based in Singapore, World Scientific has a global reach and is known for its rigorous editorial standards and beautifully produced volumes. This hardcover edition reflects the publisher’s commitment to excellence, making it a durable and valuable addition to any student’s library.

Conclusion

Plain Plane Geometry is more than just a textbook—it is a gateway to the enchanting world of geometric reasoning. Whether you are a student aiming to excel in competitive exams, a teacher looking for stimulating material, or a lifelong learner seeking the elegance of Euclid, this book will serve as a trusted guide. With its colourful illustrations, thoughtful exercises, and complete solutions, it makes geometry both accessible and deeply enjoyable. Add this premium hardcover to your collection from Bookshops.in and embark on a journey to master the plane geometry that underpins so much of mathematics and science.