Wikipedia:Reference desk/Archives/Mathematics/2006 October 15

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The Fourth Axis

Where is the forth dimension's axis? I'm refering to the spatial dimension, not time. T H L 14:56, 15 October 2006 (UTC)[reply]

In three dimensions, the standard basis includes the unit vectors (1,0,0), (0,1,0), and (0,0,1). In four dimensions, it is similar: (1,0,0,0), (0,1,0,0), (0,0,1,0), (0,0,0,1). If you are about physical space, there is no real fourth dimension, so I don't think we have the proper words to describe it in that sense. - Rainwarrior 16:54, 15 October 2006 (UTC)[reply]

There is no visual way to represent full 4 dimensions similarly to how we do with solids in three dimensions. You can project anything in higher dimensions to three dimensions, and you can take several 3-D slices of the 4-D object and then order them in time, but that's still just having your way around to represent the 4th dimension. ☢ Ҡi∊ff⌇↯ 17:30, 15 October 2006 (UTC)[reply]

I gathered that from the article, I was just wondering if they had found the axis. Apparently not. T H L 18:28, 15 October 2006 (UTC)[reply]

I'd just like to point out that modern theories say that physical space has as many as 26 dimensions, though only 3 of them are meaningful in large scales. What do you mean by "if they had found the axis"? They have found complicated explanations for more than 3 dimensions, and they have found that there is not simple explanation for them. It's not like there is any "fourth axis" hiding somewhere in the familiar euclidean 3-dimensional space. -- Meni Rosenfeld (talk) 19:17, 15 October 2006 (UTC)[reply]

I meant that I was wondering if they had found the equation of the line passing through the origin of a spatial plot at a 90 degree angle to the X, Y, and Z axes; A.K.A. the axis representing the fourth dimension. T H L 19:31, 15 October 2006 (UTC)[reply]

Well, that's easy. In parametric form, (x, y, z, w) = (0, 0, 0, t). Melchoir 19:37, 15 October 2006 (UTC)[reply]

Yeah, and it was also implicit in Rainwarrior's reply. You can also have it in equations form, which is just as simple - in 4D it's (x = 0, y = 0, z = 0), or, if you like having a single equation, |x| + |y| + |z| = 0. -- Meni Rosenfeld (talk) 20:06, 15 October 2006 (UTC)[reply]

When it comes to math, I am very blue collar. I haven't taken anything higher than Algebra 3/4, and I got a C in that. I'm not a genius. T H L 20:36, 15 October 2006 (UTC)[reply]

In that case, I suggest you read about Flatworld [1], where there is a 2D world full of 2D creatures, and the author describes how 3D objects would appear to them. By analogy, we 3D creatures can't fully comprehend the 4th physical dimension, much less the 26th. We can, however, use that dimension in science and math calcs. StuRat 22:02, 15 October 2006 (UTC)[reply]

Much thanks. T H L 04:59, 16 October 2006 (UTC)[reply]

Let me say that neither Melchoir nor I meant to offend you. I was only trying to suggest that before giving up, you should be as specific as possible about your question, and try to make sure we understand each other. Your first question made it unclear whether you are referring to a mathematical or a physical concept (and there's a world of difference!), and your second was just as vague. I get the impression you didn't fully understand Rainwarrior's reply, in which case the best thing to have done is to ask for an explanation. -- Meni Rosenfeld (talk) 13:45, 16 October 2006 (UTC)[reply]

Well, when I suggested a set of four vectors to define an axis, if you want to create the equation of a line that passes through them, there was the parametric form above, or perhaps the more familiar equation "L = A + tB" (t can be any/every real number), where "A" is some point it passes through, and "B" is a direction. In this case, "A" is (0,0,0,0), the origin (where all four axes intersect), and "B" would be (0,0,0,1) for the fourth axis. So, L = (0,0,0,0) + t (0,0,0,1). - Rainwarrior 15:08, 16 October 2006 (UTC)[reply]

I wasn't offended. I have a tendency to sound impersonal on the internet, my apologies. My vagueness was a result of my lack of understanding. I get it now, thank you both. T H L 05:28, 17 October 2006 (UTC)[reply]

Geometry - theorems and axioms

Hello, is there anywhere I could find a quite complete list of theorems in geometry (well, euclidean geometry would suffice). I looked at geometry, euclidean geometry and on pages about Hilbert's and other's sets of axioms, but couldn't find a list of theorems. I'm not really looking for very complicated theorems, just things like that the diagonals of a square intersect perpendicularily (well not just THAT simple actually :p). I would also appreciate if someone could point out where I could find a page that would compare analytic geometry and "traditional" geometry, by saying how one would state theorems and axioms in one or the other. Thanks --Xedi 19:45, 15 October 2006 (UTC)[reply]

There are thousands upon thousands of theorems in Euclidean geometry. You don't want a "quite complete" list, I hope. But in any case, I don't know of a list of even "notable" geometrical theorems. As to the comparison between analytic geometry and "traditional" (axiomatic) geometry: the difference is not so much in how you state the theorems but in how you go about proving them. For traditional geometry you have Euclid's axioms (Euclidean geometry#Axiomatic approach). For analytical geometry you could use any axiomatization of the real numbers, but no working mathematician thinks in terms of axioms when proving geometrical results analytically. --Lambiam ^Talk 23:05, 15 October 2006 (UTC)[reply]

HOW DO I ADD AUTO TIME.

HOW CAN I ADD AUTO TIME TO MY CALC. I WOULD LIKE TO SIGN PEOPLE IN AND OUT AND KNOW HOW LONG THE WAIT WAS BY CLICKING A CLOCK ICON. PEGGY [email removed] —Preceding unsigned comment added by 68.88.141.66 (talk • contribs)

Please don't write in ALL CAPITAL LETTERS.
Do not include your e-mail address.
Sign your question.

And most importantly, we can't answer your question unless you:

Be specific.

--Ķĩřβȳ ♥Ťįɱé Ø 21:30, 15 October 2006 (UTC)[reply]