How to calculate the area of a 4 dimensional curve?

Question

I have been searching on Google about it, and I found that given a sample, 4 points, per example, I could find a function and use integral on it.

I am sorry if it sounds silly, I am very dummy in mathematics. How could I find the area of this curve?

I want to know the length of the trajectory of the center of an object moving in 3-dimensional space.

Could you clarify what you're trying to do? Curves don't have area. — Antonio Vargas, Aug 22 '14 at 21:43
Sorry, well, perhaps you can help me with, then: I have a four dimensions chart: height, width, depth, and time. I would like to know how much an object was moved, during a time lapse. — marcelo-ferraz, Aug 22 '14 at 21:48
so you want to know the length of the trajectory of the center of an object moving in 3-dimensional space? — mike, Aug 23 '14 at 00:38
How do you define the curve? (Just by four points on the curve?) — Tunococ, Aug 23 '14 at 01:46
As I am analysing per sample, per example 4 or 5 at each time, I could use a line, instead of a curve. — marcelo-ferraz, Aug 23 '14 at 01:52
I think it would be simpler and not astray too much from the real data — marcelo-ferraz, Aug 23 '14 at 01:53

score 0 · Accepted Answer · answered Aug 25 '14 at 20:10

0

In the comments they helped. I've found the solution: √((x2−x1)^2+(y2−y1)^2+(z2−z1)^2)

It was just a simple case of of getting the length of 3d diagonals.

Thank you very much for the help.

answered Aug 25 '14 at 20:10

marcelo-ferraz

1

I think you may be more interested in this: http://en.wikipedia.org/wiki/Arc_length#Finding_arc_lengths_by_integrating – jameselmore Aug 25 '14 at 20:14
Wow, I am amazed... – marcelo-ferraz Aug 29 '14 at 17:28

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