Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Compared to the concept of geodesics the concept of quasi-geodesics seems to be substantially harder to grasp and digest. I was given a promising hint to the concept of quasi-geodesics here but the usual references didn't reveal something like an "easy access" to the concept:

So I am still looking for something like a "gentle introduction to quasi-geodesics".

share|cite|improve this question
The Wikipedia and EoM articles to which you linked discuss two unrelated concepts that go by the same name "quasi-geodesic". One, defined in Wikipedia, is useful in negatively curved (hyperbolic) spaces. The other, described in EoM, is mostly used in positively curved (Alexandrov) spaces. – user53153 Feb 2 '13 at 2:45
up vote 4 down vote accepted

This is rather self-serving, but I do discuss quasigeodesics in my book with Erik Demaine, Geometric Folding Algorithms: Linkages, Origami, Polyhedra, pp.372-380. I spent some time absorbing the Russian geometry literature before writing that section. Some of the same material is revisited in a more elementary presentation in my book with Satyan Devadoss, Discrete and Computational Geometry, pp.200-205:
Figure 6.35
I would be interested myself if there is a more "gentle introduction." I don't think so. And at least the way I have presented it in these books, it is, I think, rather easy to understand.

share|cite|improve this answer
:Thank you very much! I'll try to get your book. – Hans Stricker Feb 2 '13 at 10:28

I read from Vandereycken's PhD thesis ( that quasi-geodesics are first order approximations, also called retractions (used in optimization). It is a cheap approximation to a geodesic.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.