Advanced Euclidean Geometry (Dover Books on Mathematics) by Roger A. Johnson (PDF)

Description

For many years, this elementary treatise on advanced Euclidean geometry has been the standard textbook in this area of classical mathematics; no other book has covered the subject quite as well. It explores the geometry of the triangle and the circle, concentrating on extensions of Euclidean theory, and examining in detail many relatively recent theorems. Several hundred theorems and corollaries are formulated and proved completely; numerous others remain unproved, to be used by students as exercises.The author makes liberal use of circular inversion, the theory of pole and polar, and many other modern and powerful geometrical tools throughout the book. In particular, the method of “directed angles” offers not only a powerful method of proof but also furnishes the shortest and most elegant form of statement for several common theorems. This accessible text requires no more extensive preparation than high school geometry and trigonometry.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book was written in the 1920s, and while I don’t think that it’s outdated, its emphasis may be misplaced. It’s dense in theorems, etc., but it has very few diagrams and many of the theorems are difficult to understand without those diagrams. Its proofs are terse and many of the included diagrams are read with difficulty, as the small-letter subscripts are difficult to differentiate. Finally, it’s index is small and if you’ve forgotten some definition and want to look up the term, you’ll generally not find its reference in the index.The book does a deep dive into triangles, quadrilaterals, inscribed figures, polygons, circles and some inversive geometry. and generally ignores some other things like conic sections–ellipse, parabola, hyperbola. What it does cover, it covers in depth, but I would have preferred less depth and a more wide-ranging discussion.

⭐If you enjoyed proofs in high school geometry, this will be a pleasure to work through. Without being bogged down by calculations or coordinates, this book presents some of the more famous (to contest participants) and advanced theorems of Euclidean geometry. This should be required for anyone working towards olympiad level geometry and any math team coaches. Be warned that, though still a minority in terms of the type of problems, this book has no constructions. For that, I recommend (albeit reluctantly due to a lack of better alternatives) Altshiller-Court’s College Geometry.Previous reviewers are correct to say that most of the problems are just proofs of stated theorems, but that is what most higher math textbooks do. You’ll be surprised to find, though, that even just those proofs are sufficient to cement the knowledge found in this cheap and small book in your head. For a variety of applications and more interesting exercises, a next step with this material (though more of a lateral move in terms of content and downwards move in terms of difficulty) is Coexeter’s Geometry Revisited.This book assumes a STRONG background in high school geometry.

⭐I am loving the book so far, the only problem I have run into is that there are odd words throughout the book When I googled the words, I found simpler versions, I suppose that is just the world of old school Geometry.

⭐A median book, of no use either in classroom, nor for enthusiastic student.No gain in achieving it.

⭐Recently Dover has reissued two classics on Euclidean geometry,

⭐and this book. Both books were originally issued in the first half of the 20th century and both were aimed at a college level audience. Both of them also have a considerable amount of so called triangle geometry. As triangle geometry has seen a large upsurge the last years, especially during the last two decennia, there is certainly a need for an English book that gives an overview of the subject including the recent results. These books are useful in this respect but as they are both from the first half of the 20th century, they are out of date. Until a modern treatment of the subject will be available, these two books and the resources on the www will have to do. Altshiller Courts’ book has a great set of exercises that can be used as a training ground for geometric problem solving. The problems in Johnsons’ book mostly ask for proofs of theorems that are ommited in the text (that’s why I give 4 stars). Another drawback of Johnsons’ book is that there is no attention paid to geometric constructions. If you are interested in the subject, buy both, its certainly value for money.The book assumes that you are familiar with simple geometrical concepts like congruence of triangles, parallelograms, circles and the most elementary theorems and constructions as can be found in Kiselev’s book

⭐.The table of contents:I Introduction Prerequisites Points at infinity Notation Directed anglesII Similar Figures Homothetic figures Centers of similitude of two circles Similar figures in generalIII Coaxal circles and inversions The radical axis Coaxal circles InversionsIV Triangles and Polygons Ratios in the triangle Quadrangles and quadrilaterals The theorem of Ptolemy Triangle and quadrangle theorems Polygon theorems and exercises Theorems concerning areasV Geometry of Circles The power theorem of Casey Circles of antisimilitude Poles and polars Stereographic projectionVI Tangent Circles Circles tangent to two circles Steiner chains; the arbelos The problem of Apollonius Four circles touching a circleVII The theorem of Miquel The Miquel theorem Pedal triangles and circles; Simson linesVII Theorems of Ceva and Menelaos Theorems of Ceva and Menelaos; applications Isogonal conjugatesIX Three Notable Points Fundamental properties of orthocenter and circumcenter The orthocentric system Properties of the median point The polar circleX Inscribed and Escribed Circles Fundamental properties Algebraic formulas; principle of transformationXI The nine point circle Properties of the nine point circle The theorem of Feuerbach Further properties of Simson linesXII Symmedian Point and Other Notable Points Symmedians and the symmedian point The isogonic centres Nagel point, Spieker circle, Fuhrmann circleXIII Triangles in Perspective The theorem of Desargues The theorems of Pascal and BrianchonXIV Pedal Triangles and Circles Pedal triangles and circles of a quadrangle Fontené’s theorems; the theorem of Feuerbach The orthopoleXV Shorter Topics Statical theorems: center of gravity, resultant of vectors The cyclic quadrangle and its orthocenters The theorem of Morley Circles of Droz-Farny Miscellaneous exercisesXVI The Brocard Configuration The Brocard points and their properties The Tucker circles The Brocard triangles and the Brocard circle Steiner point and Tarry point Related trianglesXVII Equibrocardal Triangles The Neuberg circles Vertical projection of triangles Circles of Appolonius and isodynamic points The circles of Schoute Generalizations of Brocard geometryXVIII Three Similar Figures Similar figures on the sides of a triangle Three similar figures in generalIndex

⭐accurate and speedy

⭐Great Price!!!

⭐Nice, classic treatment. Everything you wished you had learned after your first course in geometry.

⭐very interesting results and simple exposition. A must read for people interested in the topic.

⭐A great well-written comprehensive guide in advanced Euclidean geometry. It’s pretty hard to understand at first, but if you draw many pictures and think well of the theorems and definitions you will learn a lot!

⭐This is a reprint by Dover of a very good book about Euclidean geometry. But the initial edition went with various typos. I don’t understand why, with today’s technical possibilities, the editor cannot correct them after scanning and before doing the reprint. I am sure the author, if he could see it, would not find such corrections to the original edition a lack of respect, all the contrary.Some typos are obvious but not all, especially when they appear in a figure (see the attached samples)

⭐book arrived on time, and physically as described.About the book’s contents:It’s a very nice sequel to high-school geometry. Contains many, many theorems and properties that will help solve geometry problems.Highly recommended.Do be aware that the book was written in 1929, and that the book was slightly short of illustrative figures, the sketching of which was recommended as exercise for the reader.

⭐Received on time, at advertised,

Keywords

Free Download Advanced Euclidean Geometry (Dover Books on Mathematics) in PDF format
Advanced Euclidean Geometry (Dover Books on Mathematics) PDF Free Download
Download Advanced Euclidean Geometry (Dover Books on Mathematics) 2007 PDF Free
Advanced Euclidean Geometry (Dover Books on Mathematics) 2007 PDF Free Download
Download Advanced Euclidean Geometry (Dover Books on Mathematics) PDF
Free Download Ebook Advanced Euclidean Geometry (Dover Books on Mathematics)