Math and Science Questions

[Tempestas]

Firstly: What is non-Euclidean Geometry? After attempting to read the wiki article, I only have two new peices of information: A) It has something to do with curved surfaces and B) the Parallel Postulate.

Secondly: I've been interested in assorted theoretical physics such as Quantum Physics, the fourth dimension, tessaracts, etc. recently. I've read about the double slit experiment, Shrodinger's Cat, releativity, and flatland. What other things should I see/research that would continue in these fields? Articles that don't require extensive background knowledge of certain sciences or math (In 8th grade science and Geometry) would be appreciated.

 

[fullerene]

I don't know a ton about math-theory-stuff, but I'm guessing that there are lots of different non-Euclidean geometry. I only learned (very briefly, bits of) one other type of geometry--spherical. The general idea was something along the lines of "if you translated a plane into a sphere, what would things look like?" A line, previously extending infinitely far in both directions, would eventually wrap back around on itself, creating a circle around the sphere. Line segments (straight bits that don't extend off to infinity) are like arcs along the surface of the sphere. Things like "triangles" (though the sides are curved, of course) can be constructed with three right angles, and lots of other weird stuff like that.

I'm sure there's a more "mathy" answer... but I'm a physicist, not a mathematician, so I don't deal well with all their formalities, axioms, etc.

As far as physics goes: I haven't tried it yet, but one of the sites to one of my classes (physics lab at a university) linked to a site which looked interesting, http://www.anu.edu.au/Physics/Searle/index.html

It's supposed to be a really good visualization of Special Relativity. What would the world look like if we could move close to the speed of light?


I'm not sure if they'll be understandable to you yet, but I also found the Stern-Gerlach Experiments extremely... ridiculous. Quantum Mechanical principles say that measuring the state of something actually changes the system. Almost like the old philosophical question, "if a tree falls in the forest and no one's around to hear it, does it make a sound?" The Stern-Gerlach experiments tested this type of thing on the angular momentum of particles, feeding them through magnetic fields. The magnetic fields were designed so that particles spinning in one direction would be deflected one way, and particles spinning in the other direction would deflect the other.

By setting these machines in various series' (and aligning them in different ways), they came up with some very cool results that made me "wtf?" the first time i heard them.

 

[Latro]

Euclid had a bunch of axioms for Euclidean geometry, though I think he called them Postulates. As I recall there were 5 of them. Non-Euclidean geometries arise when you allow one or more of them to be false. This allows counterintuitive geometric constructions, such as triangles with 3 right angles, or "lines" that intersect in infinitely many places without being the same line.

As for learning advanced physics on your own...it won't be easy, but the books exist. Don't expect it to go fast; at my uni QM is first introduced to 2nd year physics students, and there is QM all the way up into the 700 level (advanced grad school) classes.

 

[fullerene]

ah... yeah. Here they are, btw

http://en.wikipedia.org/wiki/Euclidean_geometry#Axioms

 

[Agent Intellect]

A good place to start for some interesting, lay-man friendly theoretical physics is Brian Greene's "The Fabric of the Cosmos" (to a lesser extent, "The Elegant Universe", which talks mainly about string theory and can be watched as a NOVA special) and Brian Cox and Jeff Forshaw's "Why Does E=mc^2". "The Universe in a Nutshell" by Hawking is good, too (I think it's a lot better than "A Brief History of TIme" especially since it has pictures).