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I'm looking for suggestions of books on inequalities and geometry.

I'm specifically asking this because I'm not looking for a book that is suited for students preparing for mathematics competition. I won't mind the books having a good bunch of approachable and challenging questions, but I'm looking for a book for personal edification, and reviewing and building on the basics which are usually taught in a not-so-rigorous and complete manner in high school.

Junaid Aftab
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4 Answers4

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This one is oriented towards competition level Geometry:

$\qquad$Kedlaya -- Geometry Unbound (2006)

Moreover, the author made it freely available:

$\qquad$http://kskedlaya.org/geometryunbound/gu-060118.pdf

Here's one from AoPS, also free:

[Members of Mathlinks] -- Geometric Inequalities Marathon 1 - The First 100 Problems and Solutions (2011)

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0ahUKEwiQ45GGlZHUAhUB4yYKHSBNDbEQFggxMAA&url=http%3A%2F%2Fkskedlaya.org%2Fgeometryunbound%2Fgu-060118.pdf&usg=AFQjCNExuDbA2Tjx1IcoVd4gCKdWtbT9ww&sig2=X_H11SC0dz5HvBHHiynQQQ&cad=rja

It downloads to a file called "Geometry", with no extension, so you may need to rename it so that the extension is ".pdf"

quasi
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A great and insightful book on inequalities of various type is the book:

Inequalities

of G. H. Hardy, J. E. Littlewood and G. Pólya.

I especially like it as it explains also the underlying mechanism behind inequalities. It gives also a great overview of all types of means inequalities as well as their generalizations (in many different directions).

Surb
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  • Yes, I was looking at this book just yesterday. The book seems great, but I was looking for another book before covering Hardy's book. Also, I think it's one of the books that should be covered if one has some time on one's hand. Like Hardy's other textbooks, the book seems to be a huge exercise. Any other suggestions? – Junaid Aftab May 27 '17 at 23:26
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Surprisingly not yet mentioned is Volume #4 in the well known New Mathematical Library series:

Geometric Inequalities by Nicholas D. Kazarinoff (originally appeared in 1961) see here also

Also in this series (Volume #3) is

An Introduction to Inequalities by Edwin F. Beckenbach and Richard E. Bellman (originally appeared in 1961) see here also

Dave L. Renfro
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You can try Advanced Olympiad Inequalities: Algebraic & Geometric Olympiad Inequalities, it deals with both algebraic and geometric inequalities. The book contains around 300 solved problems with more than one solutions for many problems. It has also a variety of unsolved problems that were left as extra challenges to the reader.

YuiTo Cheng
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Olympiados
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