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 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)?