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A function for a line in a square (or a triangle or a etc) 
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#1
Nov2412, 04:55 AM

P: 80

I don't have one off the top of my head (my maths is very rusty) but I think that ,starting from a cartesian point it is possible to create a function that allows one to draw a polygon in 2 or 3(?) dimensions.
This object is idealised and perhaps does not exist in the "real" world . Is it possible to create a corresponding function (for the simplest of those examplesmaybe just a line or even a point but ideally a triangle or a square) that would stand up in the "real" world? For example ,if we assume that the line is "drawn" at the speed of light (or half the speed of light) can this new function be created that would incorporate the speed of the creation of the polygon? Of course this is still idealised since it does not take into account gravity but could the polygon be made from matter that had no mass(photons?) that would get around this or woulo the curvature of space have to be part of the function also? So most simply is there a function to describe ,say, a triangle in a way that is "real" but not idealised (in a cartesian way)? EDIT:I realise that this is a calculation that is done routinely as that is how we can send rockets to the moon and beyond .But are those calculations done by performing millions of calculations to calculate the position of the spacecraft as it approaches its desination? I mean is the "journey" divided up into very small segments (in time) and are these all added together in the computer to calculate the trajectory  in the same way as I imagine the weather and climate change is forecast by adding together calculations corresponding to small segments of time. Even so would there be a very simple example (the simplest please) of one such calculation that used mathematics (functions)? Suppose we were to send the spacecraft on a journey that sent it (ideally at the speed of light) from the left hand base of a "triangle (=the earth) to the apex of this "triangle" (= some extremely distant object) to the right hand base of the "triangle" (= another extremely distant object) and back to earth (all using slingshots of course) would there be any function that could be used to calculate this overall "triangularly shaped " journey (even approximately)? 


#2
Nov2412, 10:03 AM

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P: 12,030

Sorry, what?
Choose one: a) I completely missed a whole branch of "linedrawing physics" b) I do not understand the whole concept in your post c) something else If it is sufficient to consider two objects at a time (maybe with small perturbations of other objects), you can use analytic solutions to the equations of motion in a gravitational field as well. Look up "Kepler problem" for details. 


#3
Nov2512, 05:45 AM

P: 80

The functions used to describe trajectories seem to work incredibly well but is it fair to say that their is zero chance ,now or at any time in the future that they will be any more than approximations?
When we use functions to describe a circle,say, there is an illusion(?) that the function describes the circle perfectly but is this simply because the circle only exists in the imagination? Is it completely impossible that there could exist a function to 100% accurately predict or describe any phenomenon in nature? @mfb Perhaps the concept behind my post was to find the simplest object/event/phenomenon that exists in nuture (not in the mind) to see if there was a chance that there could be a function that describes it 100%. 


#4
Nov2512, 08:03 AM

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P: 12,030

A function for a line in a square (or a triangle or a etc)



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