books (new)

Here I am gonna recommend recent geometry books (published after 2010). So far 9 follow:

Two romantic books, one written as a proof & result collection  in triangle geometry by an amateur (Mihalescu), and one written to challenge the perception, by someone (Akopyan) who knows the present Russian Geometry problems . Also 7 olympiad oriented geometry books follow.The first of them ,written by Evan Chen, tstands out for it's unique and noteworthy approach. Τhe last is written by two Greeks, one of them, Sotirios Louridas is a famous Greek problem solver in magazines and internet forums. 

A masterpiece by a retired artillery colonel and an enthusiastic amateur mathematician, Constantin Mihalescu.

First Edition: 1955, Romanian
Second Edition: 2016, translated in English  (XYZ)

The Geometry of Remarkable Elements: Points, Lines and Circles

Author: Constantin Mihalescu   

Editors: Titu Andreescu, Dorin Andrica, Paul Blaga, and Dan Bränzei


The book we are proposing here to the English-speaking reader is one that would have qualified at the beginning of the previous century as a book of “Modern Geometry” of the triangle and quadrilateral. Most of the results were obtained in the second half of the 19th century and the first half of the 20th century. The author was a retired artillery colonel and an enthusiastic amateur mathematician. This should come as no surprise, as for any artillery officer mathematics (and, especially, geometry) plays an important part in his formation.

As the title surely suggests, this book is a rich collection of some of the most important properties of numerous points, lines, and circles related to triangles and quadrilaterals, as they were known by the mid-1950s. These include the nine-point circle, the Simson line, the orthopolar triangles, the orthopole, the Gergonne and Nagel points, the Miquel point and circle, the Carnot circle, the Brocard points, the Lemoine point and circles, the Newton-Gauss line, and many others. It was, probably, one of the most complete descriptions of the subject at the moment of the writing. The book was primarily addressed to young students but will be of interest to problem solvers in elementary geometry as well. Even geometers will find here new problems to inspire them.

related links:

Theorems without words, a touch of magic in Euclidean Geometry

Geometry in Figures: Second, extended edition

 by Arseniy V Akopyan , 232p, 2017

1st edition was uploaded free here: 

The second edition contains previous problems + 500 new

An Olympiad Geometry problem-solving book, very popular in aops, with all the theory and modern methods.

Euclidean Geometry in Mathematical Olympiads, 
by Evan Chen 2016 (MAA)


Euclidean Geometry in Mathematical Olympiads (often abbreviated EGMO, despite an olympiad having the same name) is a comprehensive problem-solving book in Euclidean geometry. It was written for competitive students training for national or international mathematical olympiads. However it has no prerequisites other than a good deal of courage: any student who is interested in the subject matter should be able to follow the exposition.

The book contains a selection of about 300 problems from around the world and is accompanied by about 250 figures.

Prerequisites and sample chapters

There are essentially no geometry prerequisites; EGMO is entirely self-contained. (This was one of the design goals.) The main limiting factor is instead the ability to read proofs; as long as you can follow mathematical arguments, then you should be able to follow the exposition even if you don't know any geometrical theorems.

Errata , samples & contents:

one olympiad geometry modern lemma book

Product Code: XYZ/19
Titu Andreescu: University of Texas at Dallas, Richardson, TX,
Sam Korsky: Massachusetts Institute of Technology, Cambridge , MA,
Cosmin Pohoata: California Institute of Technology, Pasadena, CA

Published in 2016

More info for this book:

3 olympiad geometry problem collections


Product Code: XYZ/3
Titu Andreescu: University of Texas at Dallas, Richardson, TX,

Michal Rolinek: Institute of Science and Technology, Klosterneuburg, Austria,

Josef Tkadlec: Charles University, Prague, Czech Republic
Published in 2013

Product Code: XYZ/4
Titu Andreescu: University of Texas at Dallas, Richardson, TX,

Michal Rolinek: Institute of Science and Technology, Klosterneuburg, Austria,

Josef Tkadlec: Charles University, Prague, Czech Republic
Published in 2013

Titu Andreescu: University of Texas at Dallas, Richardson , TX,

Cosmin Pohoata: Columbia University, New York, NY
Published in 2014

More info for those 3 books:

A recent Transformation Geometry book . with famous results proved in new ways

Classical Geometry: 
Euclidean, Transformational, Inversive, and Projective 
by I. E. Leonard, J. E. Lewis, A. C. F. Liu, G. W. Tokarsky  2014


Features the classical themes of geometry with plentiful applications in mathematics, education, engineering, and science

Accessible and reader-friendly, Classical Geometry: Euclidean, Transformational, Inversive, and Projective introduces readers to a valuable discipline that is crucial to understanding bothspatial relationships and logical reasoning. Focusing on the development of geometric intuitionwhile avoiding the axiomatic method, a problem solving approach is encouraged throughout.

The book is strategically divided into three sections: Part One focuses on Euclidean geometry, which provides the foundation for the rest of the material covered throughout; Part Two discusses Euclidean transformations of the plane, as well as groups and their use in studying transformations; and Part Three covers inversive and projective geometry as natural extensions of Euclidean geometry. In addition to featuring real-world applications throughout, Classical Geometry: Euclidean, Transformational, Inversive, and Projective includes:

Multiple entertaining and elegant geometry problems at the end of each section for every level of study
Fully worked examples with exercises to facilitate comprehension and retention
Unique topical coverage, such as the theorems of Ceva and Menalaus and their applications
An approach that prepares readers for the art of logical reasoning, modeling, and proofs

The book is an excellent textbook for courses in introductory geometry, elementary geometry, modern geometry, and history of mathematics at the undergraduate level for mathematics majors, as well as for engineering and secondary education majors. The book is also ideal for anyone who would like to learn the various applications of elementary geometry.

Related links

An Olympiad journey through problem solving written by 2 Greeks, one of them, Louridas is a famous problem solver in magazines and internet math forums

Problem-Solving and Selected Topics in Euclidean Geometry.

In the Spirit of the Mathematical Olympiads

Louridas Sotirios E., Rassias Michael Th.

Springer 2013, pages 235

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