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16 votes
2 answers
2k views

There are two points on the Earth's surface that ... ?

At every moment in time, there are two points on the Earth's surface that have the same $\lbrace x, y, z, ... \rbrace$...? What is the strongest, most impressive statement one can make here? The ...
1 vote
0 answers
190 views

what belongs in a first university-level geometry course? [closed]

I know this is not really a research question, but I would like to ask it of research mathematicians, to see if there is a consensus. In a recent discussion on this topic, someone suggested that if ...
23 votes
12 answers
15k views

Textbook for undergraduate course in geometry

I've been assigned to teach our undergraduate course in geometry next semester. This course originally was intended for future high-school teachers and focused on axiomatic, Euclid-style geometry (...
8 votes
2 answers
2k views

What is the best *general triangle*?

During courses on geometry it is sometimes necessary to draw a triangle on the blackboard that can easily be recognized as a general triangle. It must not be rectangular and must not have two or more ...
3 votes
2 answers
957 views

Simple definition of the Hausdorff measure using squared paper

I am giving a "non-technical" seminar in which I would like to give an elementary introduction to the Hausdorff dimension and measure. For simplicity, I was hoping to give a more intuitive ...