2
votes
3answers
224 views

Book with lots of geometry theorems

I want to study geometry and was looking for some book that has lots of theorems and covers almost all Euclidean geometry that is needed for High School and Maths Olympiads. Thanks.
1
vote
1answer
61 views

examples of toy non-Euclidean geometries

Today I was working on a problem in euclidean geometry, and I found it immensely useful to compare with Fano geometry, for contrast. Are there any other toy geometries like Fano geometry? I think it ...
19
votes
9answers
3k views

What is the simplest proof of the pythagorean theorem you know? [duplicate]

Maybe enough so to explain it to children.
-3
votes
5answers
389 views

Examples of $ \sqrt 2$ and $\sqrt[3]{3}$ in nature?

The question has been written up. By nature i mean in physics, ascetics, etc. @all. I expected some advanced things, the things all of mentioned are already known to the asker.
3
votes
5answers
280 views

Geometry books with beautiful diagrams

What are some geometry books with particularly beautiful diagrams? Old or new. Could be on 'standard' material or specialised on one particular topic. Something for the connoisseur of mathematical ...
16
votes
5answers
641 views

What Mathematics questions can be better solved with concepts from Physics?

Over the years, I've seen several questions in mathematics that can be solved using concepts borrowed from Physics. Having seen these question, I'm interested to find out what other mathematics ...
2
votes
2answers
85 views

What are some alternative ways of describing a Tetrahedron rather than using 4 points?

What are some alternative ways of describing a Tetrahedron rather than using 4 points? This question made me wonder besides using the four points following methods could also be used to describe a ...
0
votes
2answers
53 views

Is there any significant Geometric/analytic property of the Pearson coefficent that could be applied to statistics?

Is there many significant Geometric/analytic property that the Pearson coefficent has which could be applied to statistics? It seems very interesting to me. Thanks in advance.
0
votes
2answers
71 views

Is there plane curves with limit number of operations in which is non-constructible and how do we prove it

Is there plane curves with limit number of operations in which is non-constructible and how do we prove it is non-constructible, i call it non-constructible if we have to plot infinity number of point ...
19
votes
2answers
811 views

Geometric proof for inequality

While on AOPS, I saw this interesting problem. I was wondering how many different approaches could be used to tackle the problem. In other words I am looking for interesting and unique ways to solve ...
14
votes
9answers
3k views

What are some good iPhone/iPod Touch/iPad Apps for mathematicians?

There are lots of good apps for teaching mathematics to children but I would like to learn about apps for undergraduate/graduate/research levels. Helper questions Any algebra system (like ...
3
votes
2answers
136 views

How can an object grow so that the ratio of surface area to volume remains constant?

Obviously there are many applications for this and many solutions. I am also interested in closed curves that have the same ratio of area to arc length as we "grow" them, growth is done by ...
10
votes
5answers
530 views

What are the postulates that can be used to derive geometry?

What are the various sets of postulates that can used to derive Euclidean geometry? It might be nice to have several different approaches together for comparison purposes and for ready reference. It ...
13
votes
4answers
709 views

Developing the unit circle in geometries with different metrics: beyond taxi cabs

My class had a good time redeveloping the unit circle under the taxicab metric. Now some of them want to do it again with another similar metric. I want to give this to some of my "honors" ...
64
votes
19answers
28k views

Software for drawing geometry diagrams

What software do you use to accurately draw geometry diagrams?
38
votes
15answers
8k views

What is the most elegant proof of the Pythagorean theorem?

The Pythagorean Theorem is one of the most popular to prove by mathematicians, and there are many proofs available (including one from James Garfield). What's the most elegant proof? My favorite ...