Take a sheet of elastic material, like a balloon, but square. Suspend the corners in clamps on posts so that it’s “perfectly” flat. Draw a line that is the shor

Take a sheet of elastic material, like a balloon, but square. Suspend the corners in clamps on posts so that it’s “perfectly” flat. Draw a line that is the shortest distance between two points on the material: it will be a “straight” line like what you learnt in geometry class. Now place a marble in the center of the sheet and let it stretch the sheet. Now draw the shortest possible line connecting these two points: it will curve (and unless you chose by coincidence) it will likely not overlap with the first line: the “shortest distance” between the points has changed. There’s another aspect to this: the expansion coefficient. One such model is that the coefficient depends only on time: as time passes, distances increase. To model this, draw the same line on the flat sheet of material, then expand it uniformly in all directions. The distance is still a straight line, but the line is longer after the expansion.