Archive for the ‘Geometry’ Category

Notes on discrete and polyhedral geometry

Friday, August 28, 2009 10:04
Posted in category Combinatorics, Geometry, Notes

Problems in discrete geometry (i.e. the border between combinatorics and geometry) have made several recent appearances on the IMO (typically, granted as Q6). A nice book by Igor Pak covers much of the important material in this area — the book is aimed at undergaduate and graduate students in maths, but the first few chapters in particular are suitable for Olympiad level students.

As in many cases, the important thing is not the results themselves (though Helly’s theorem is a useful tool in lots of setting) but the “style” of proofs in this area.

Michael

Transformational geometry

Tuesday, April 21, 2009 22:50
Posted in category Geometry

Here are the notes from Arkadii Slinko’s Auckland squad lecture last weekend. They present solutions to ten geometric problems — some from contests, some classical.  The common theme is the use of geometric transformations.

Solutions to some of the problems are available, and can be obtained by writing to nzmathsolymp@gmail.com.

Geometric inequalities

Tuesday, April 21, 2009 18:20
Posted in category Geometry

These notes by Arkadii Slinko are a gentle introduction to geometric inequalities, with many nice examples.

Solutions to some of the problems are available, and can be obtained by writing to nzmathsolymp@gmail.com.

Collinearity and concurrence

Sunday, March 22, 2009 20:18
Posted in category Geometry, Notes

These geometry notes by Heather Macbeth come from the last month’s Auckland olympiad squad training.  They cover some techniques for proving collinearity and concurrence.  Along the way they prove all your favourite triangle geometry theorems, and do some cool things with homotheties and reflections.

An orthogonality lemma

Tuesday, December 16, 2008 17:30
Posted in category Geometry

These notes by Heather Macbeth discuss a useful criterion for the orthogonality of two line segments.  They’ll also give you some practice using vectors for geometry.