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I am planning to take a graduate Geometry course next semester. The preliminary syllabus does not specify any textbook but has the following descriptions:

Catalog Course Description: This course studies higher geometry including triangulations of polygons, Voronoi diagrams and Delaunay triangulation, algorithms in computational geometry, Euler characteristic of geometric objects, conics, elements of differential geometry of curves.

Topics Covered: inequalities, Helly's theorem, power of a point, inversion, Voronoi diagrams and Delaunay triangulations, algorithms in computational geometry, Euler characteristic of geometric objects, conics and their affine and metric classification, elements of differential geometry of curves, polyhedra.

I would like to study early taking advantage of my downtime. Is there any textbook that you would like to recommend for my self study?

Thank you very much for your time and pointers.

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The topics you list are usually in the field called discrete geometry. A nice text in the area is Devadoss and O'Rourke's Discrete and Computational Geometry. I have not used it myself, but know folks who have and liked it quite a lot. It covers most of your topics (absent, in particular, is Helly's theorem).

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  • $\begingroup$ @A.Magnus Since you haven't accepted answers before, you might not know, but if your question is resolved by one of the answers, you can click the checkmark below the score on the left to accept it. This takes the question off the 'unanswered' list and gets both you and the user you accepted a little reputation. $\endgroup$
    – user98602
    Commented Apr 7, 2014 at 14:12
  • $\begingroup$ I just did it, apologize for being ignorant. What are those up and down arrows above the check mark for. Thanks again. $\endgroup$
    – A.Magnus
    Commented Apr 8, 2014 at 14:34
  • $\begingroup$ @A.Magnus No worries, we were all new once :) The up and down arrows are to upvote and downvote a post; a user gets rep if you upvote and loses rep if you donwvote. Generally downvoting is reserved for answers that are mathematically incorrect rather than unhelpful answers, but you can upvote as much as you want. $\endgroup$
    – user98602
    Commented Apr 8, 2014 at 16:13

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