Geometry of the Triangle

Abstract

Triangle geometry is a captivating yet often overlooked subject in high school and university curricula. This book offers a clear and engaging introduction, presenting the fundamental lines, points, and circles associated with the triangle in an accessible and visually compelling way.

Theorems and proofs are carefully developed with no steps omitted, ensuring clarity and ease of understanding. A wealth of full-color illustrations enhances the mathematical reasoning, making even complex concepts intuitive.

Requiring only basic knowledge of school geometry, this book unveils surprising and elegant connections within triangle geometry. Readers will explore key topics, including the Euler line, nine-point circle, symmedians, halfway points, and more, each presented in a structured and reader-friendly manner.

With a gentle yet thorough approach, the text guides readers through the Simson line, mirror triangle, Fuhrmann circle, splitters, cleavers, and other remarkable properties of the triangle. The unexpected relationships between these elements are revealed in a way that is both engaging and easy to follow.

This book is an ideal introduction for both students and professional mathematicians, offering a visually rich and intellectually rewarding journey into the fascinating world of triangle geometry. It takes the reader through the theory in a leisurely and transparent manner and carefully presents the theorems and proofs.

About the Author

Jens Carstensen has taught mathematics at high school/college level for over 40 years in Denmark. He is the author and co-author of several successful textbook systems and is currently continuing this work. He has been the editor of a Problem Corner for 40 years and has published and edited a small mathematics magazine, thereby obtaining a wide experience of writing mathematics for both students and professional mathematicians.