Euclidean Definition and 214 Threads

"Surface Volume" in 4-d graph: Euclidean Geometry Question Suppose you have a smooth parametrically defined volume V givin by the following equation. f(x,y,z,w)= r(u,s,v) = x(u,v,s)i + y(u,v,s)j +z(u,v,s)k + w(u,v,s)l Consider the vectors ru=dr/du, where dr/du is the partial...

Suppose you have a smooth parametrically defined volume V givin by the following equation. f(x,y,z,w)= r(u,s,v) = x(u,v,s)i + y(u,v,s)j +z(u,v,s)k + w(u,v,s)l Consider the vectors ru=dr/du, where dr/du is the partial derivitive of r with respect to the parameter u. Similarly, rv =...

Why does everyone use +---/-+++ Minkowski spacetime over ++++ Euclidean spacetime? Minkowski spacetime preserves spacetime intervals under Lorentz transformations but so does Euclidean spacetime under equivalent rotational transformations from which SR can also be deduced. (someone show me how...

Stephen Hawking's latest preprint on Arxiv uses "Euclidean Quantum Gravity". In fact, he says: "I adopt the Euclidean approach [5], the only sane way to do quantum gravity nonperturbatively." http://www.arxiv.org/abs/hep-th/0507171 Any comments? Carl

hi, for most of you this might be a simple question: Is it possible to embed the flat torus in Euclidean space? If we, for example, take a rectangle and identify the left and the right sides we get a cylinder shell, that can be embedded easily in R^3. If we construct the...

this seems to be a very fundamental problem...but i need help... prove or disprove : let D be a euclidean domain with size function d, then for a,b in D, b != 0, there exist unique q,r in D such that a= qb+r where r=0 or d(r) < d(b). first of all, what is size function? next...do we only...

If you had line AB is parallel to BC and BC is parallel to CD, is AB parallel to CD? ----> Not if AB=CD since a line (at least in Euclidean Geometry) cannot be parallel to itself. How would you prove that AB is not line CD? PLEASE NOTE: Base all your input in the realm of Euclidean...

Ted Jacobson has been developing a theorum using only the principle of Relativity and Euclidean Geometry:http://arxiv.org/abs/gr-qc?0407022 Having followed his papers for some time I have to say its quite amazing(this paper more so!), but I have found a flaw in this evolution paper.

A triangle in Euclidean space can be described as having a hypotenuse of one, and legs of Lorentz parameters \beta and \gamma. What spatial curvature underlies a triangle with hypotenuse one, and legs 1/ \beta and 1/ \gamma?

I need to be able to plug in appropriate x and y values for: 154x + 260y = 4 I guess this is done by working the euclidean algorithm backwards. But how do you do that?

Hi everyone, i have to do a general math project for my math course. It is nothng special, just a proof of a theorem on my choice and a bit of history and interesting facts. I kind of decided to do it on non-euclidean geometry, because it is fun. Now my question: does anybody know a good...

I am little confused on this issue, actually the thing that is confusing me is my book. We all know the formula m=qn+r and 0<r<n In the formula we go until r=0, then you will know relativley prime. When given a problem, for example, (862,347) we have m=862 while n=347 so we have the...

I was at brunch this morning and I met a young man of about 35 years who is a musician but studied mathematics in college. He mentioned to me that one of the great problems of mathematics is the problem of trisecting the angle. He taught me how to bisect an angle, and kept emphasizing that...

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