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

[geordief]

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

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 examples-maybe 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 realize 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)?

 

[mfb]

Sorry, what?

Choose one:
a) I completely missed a whole branch of "line-drawing physics"
b) I do not understand the whole concept in your post
c) something else

EDIT:I realize 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?

That is a common concept.
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.

Even so would there be a very simple example (the simplest please) of one such calculation that used mathematics (functions)?

Every calculation uses functions.

(ideally at the speed of light)

No matter can travel at the speed of light.

would there be any function that could be used to calculate this overall "triangularly shaped " journey (even approximately)?

Sure. If the gravitational influence of everything beside one object is negligible, the spacecraft will follow a conic section.
Look up "Kepler problem" for details.

 

[geordief]

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%.

 

[mfb]

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?

As there are no general, analytic solutions for trajectories in general relativity, all calculations will be approximations - even if you do not consider the finite size of all objects and quantum mechanics.

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?

No, there is the knowledge that the circle is a good approximation to something in our world. A circle as mathematical object can be described exactly.

Is it completely impossible that there could exist a function to 100% accurately predict or describe any phenomenon in nature?

The common view is that there is a small set of fundamental laws of nature - probably something you can write down on a sheet of paper. If that exists, it would describe everything, but our methods to measure the current state of the universe and our ability to evaluate its evolution (based on those laws) are limited.