Pi

 While that's technically true, I don't think you realize how much evidense there is for relativity. Finding Eistein to be wrong is about as likely as disproving the existance of gravity at this point.

However, since the universe is practically empty, Euclidean geometry is really accurate, as long as you're not talking about a circle that's right next to a black hole or something.

Yes i know very good what Ευκλειδης said,he is an ancestor of me!But everything he was claimed counted on perfect shapes.Anyway,as you said "we have been presented with better explanations: namely, the theory of general relativity" is something i agree.The point for me is that fractal geometry is more accurate than Euclidean,but Euclidean is much more aproachable.And finally Ευκλειδης work is a tool that people learn geometry for over 2000 years..i don't try to lower him.

Fractal geometry is far less useful than Euclidean geometry though. All you can really do with fractals (with respect to reality) is make approximate dimension counts, you can't really calculate a lot of useful information. Furthermore, even though there are a lot of natural things that are fractal-like (trees, clouds, etc.), I would say there are many more shapes on a universal scale that are better described with classical shapes. For example, the Earth is smoother than a billiard ball, so a sphere represents it almost perfectly.

Furthermore, fractal geometry really isn't different than Euclidean geometry. It still takes place (usually) in Euclidean space. All of the geometric structure is exactly the same as Euclidean geometry, it just studies "shapes" within the Euclidean space that classical geometry wouldn't bother to study. In that sense, fractal geometry is an expansion of classical geometry, not opposed to it.

 Cool, I never knew that.

I currently know 213 decimals of pi. Beat that!

janus, you're right, but Mendelbrot's fractals are still awesome to look at!

 Absolutely. I can't count the hours I've spent zooming in to various pieces of the Mandelbrot set.

For those who are interested: Ultra Fractal 4 is a program that displays a wide variety of fractals, and you can customize them and zoom in where you choose. They have a free trial on their website.

 I do realize how much evidence is in favor of relativity. What you don't realize is that I am not an evidentialist!

Just kidding...

Seriously though, I understand that relativity is generally accepted nowadays as a very good explanation of our universe. However, we need to remember that this was the case of Euclidean geometry not 100 years ago.

In response to your black hole comment, I assume that you are referring to gravity causing flaws in Euclidean geometry. This is one of the first discoveries that led theoretical physicists away from a Euclidean system and is what Sharukin was referring to in his original post. Don't forget, though, that the other natural forces also urge us to deviate from a Euclidean system of geometry. 

 I still don't understand this. The Euclidean system of geometry is a system much deeper than shapes and lines.

Now is a point that i wish to knew better this language.It is hard for me to express what i believe and understand good all these comments..So i borrowed an article from wikipedia from Euclidis geometry page:"However, Einstein's theory of general relativity shows that the true geometry of spacetime is non-Euclidean geometry. For example, if a triangle is constructed out of three rays of light, then in general the interior angles do not add up to 180 degrees due to gravity. A relatively weak gravitational field, such as the Earth's or the sun's, is represented by a metric that is approximately, but not exactly, Euclidean. Until the 20th century, there was no technology capable of detecting the deviations from Euclidean geometry, but Einstein predicted that such deviations would exist. They were later verified by observations such as the observation of the slight bending of starlight by the Sun during a solar eclipse in 1919, and non-Euclidean geometry is now, for example, an integral part of the software that runs the GPS system.

For me the impressive about Euclidean goemetry is if we consider when Ευκλειδης said all these things..

My opinion about general relativity is that will be accepted immortal.With chaos theory and quantum mechanics are the best tools that human ever created

Everyone knows pi. When I was in high school, I memorized e to 15 decimal places, and I still remember it: 2.718281828459045.

--Fromper 

Yeah, it is THE EXACT NUMBER OF DIGITS WIKIPEDIA GIVES YOU!