Do They Exist?

[foodchain]

My understanding of math currently is somewhat limited so if this offends anyone it was not my intention.

 

Do say functions exist like sin or cos for 4D problems? OR do such functions still apply in such dimensions with no problem? What I got this from in reading up on string theory and the 10D facet it presents. I know we have a lot of math for working 2D and 3D problems, but I guess my question is do such operators or functions exist for say 7D math problems for example, or 8D and so on.

[Klaynos]

Do you mean something like z = sin(x) + sin(y) + sin(t) ? It'd be difficult to plot, but i could carry on adding in sin(dimention) for a long long time...

[foodchain]

Do you mean something like z = sin(x) + sin(y) + sin(t) ? It'd be difficult to plot, but i could carry on adding in sin(dimention) for a long long time...

 

Is sin(t) for x,y,then z or is the t for time? See that’s what I am asking, I think:D , is that are we using functions for say 3D or 2D for xD dimensions?

 

I mean going from what I understand of GR you can’t linearly apply things all the time, can whatever axioms that say sin comes from or operates from relate to whatever axioms that GR for instance implies, or string theory for that matter? More so in the context of more then 3 or 4 dimensions?

[someguy]

Is sin(t) for x,y,then z or is the t for time? See that’s what I am asking, I think:D , is that are we using functions for say 3D or 2D for xD dimensions?

 

I mean going from what I understand of GR you can’t linearly apply things all the time, can whatever axioms that say sin comes from or operates from relate to whatever axioms that GR for instance implies, or string theory for that matter? More so in the context of more then 3 or 4 dimensions?

 

well.. sine comes from the fact that a triangle with a right angle has always the same proportion of length of sides for a given angle, in relation to that angle.

 

 

they made the radius 1 because by the law of similar triangles, that way you can multiply sin (theta) by the length of the hypotenuse of the triangle you are working with and get the correct proportion of sin (theta) for the angle x theta since 1 multiplied by any number gives that number.

 

i'm not sure if this is exactly what you mean, but if you wanted to do this but a dimension up you would have a kind of right angle prism in a sphere, where the "triangle" would have round sides so as to stay in the circle, and i don't think you can pull any neat mathematical conclusions from that, unless maybe you made a "triangle" and i do use that term extremely too loosely, that has two right angles, i'm not sure off hand if this could be in any way useful, but i'm pretty sure that if it did you could figure it out with the existing "sine.. language" ... (hardy har har har) in some formula so it would be kind of redundant. but that still wouldn't incorporate the 4th dimension like you wanted. but since this celever idea of sine language stems from geometry i don't think you could achieve that since you can't really draw in 4 dimensions, and the 4th dimension doesn't really show nice proportions like the other 3 can, unless you go relativistically speaking i guess, but i think you can use that no other way than by using complex equations so i don't think you could make a nice neat thing like the trigonometric circle can do. the best you can do is just use those functions to make more complex ones. i think the days of simple geometry are long gone and all that is left is more and more complex formulas that can sometimes reduce nicely.

 

actually come to think of it... E=mc^2 is almost exactly what you're talking about, isn't it?

 

technically time isn't really in there, but motion is pretty much time and E gives motion, so.. it's sort of there. a proportion of motion, or energy as a whole, to mass. somewhat frankensteinly a 4d sine function. yet not a sine function at all.

[foodchain]

Right but does trigonometry for instance apply via its axioms to any particular number of dimensions or is it primarily functional really in three dimensions.

[Bignose]

The angle between vectors formula is valid for any number of dimensions:

 

cos(theta) = a.b / (|a| |b|) because the dot product is valid in any number of dimensions. Therefore, you can find the angle between 10 D vectors, for example. This is about the only example I can think of, however, but there are probably many more, and this may not have been what you were looking for.

[ajb]

foodchain , do you mean something like a vector valued function?

 

[math] F: \mathbb{R} \rightarrow \mathbb{R}^{n}[/math]

[math] t \mapsto x^{i}(t)[/math]

 

 

or something more like a map

 

[math]\Phi : \mathbb{R}^{n} \rightarrow \mathbb{R}^{n}[/math]

[math]x^{i} \mapsto y^{i}(x)[/math].

 

Both can be defined.

[DanJFarnan]

8D = 8 x 2D

 

3D = 1D

 

The odd and even Balance...