What Are the Connections Between Euclidean and Non-Euclidean Geometry?

[cnrdlrud]

research topic in non-euclid geo??--Help please!

hello! I am a high school junior trying to do an independent project in geometry and I've been reading about hyperbolic geometry--or non-euclid geo in general. i now have to pose a more specific research question within the topic and i really need some help!

i do not feel that i have enough knowledge/understanding to write a paper that is compeletely about hyperbolic geometry so i want to include some kindof relativity between non-euclid and euclid(which i have a better understanding of). i also find absolute(neutral) geometry interesting--just completely ignoring the troublesome parallel postulate!

my biggest problem is that as it IS a research paper, it can't just be a list of facts that other people have discovered a long time ago. I am not smart enough to come up w/ my own discovery or anything so I am trying to at least include my own analysis and viewpoint. (how else can i be creative?)
if you have any suggestions about the research question please please reply!
thank you!

 

[fresh_42]

You could use classical results in Euclidean geometry and see how they generalize to non Euclidean geometries. E.g. Napoleon's theorem, or you can search the internet for "geometry + pdf" to find more examples.