I have read the explanation/calculation of relativistic momentum and relativistic mass in the Feynman lectures, see chapter 16.4 here: http://www.feynmanlectures.caltech.edu/I_16.html. (I guess this explanation goes back to Lewis/Tolman.)
The argument seems to use two spatial dimensions in order to make the situation of the elastic collision of two objects with the same rest mass not too symmetric. My question is whether there is a similar argument that already works in one spatial dimension.
Please note that I am not looking for a more sophisticated explanation using four-momentum (or rather two-momentum in 1+1 dimensions), although it will be much more elegant mathematically.