This table mat I have done using circles of double crochets. For making it thick, so that hot pots can be placed on it, I have done the dc, over a long chord, covering it with the stitches.
To maintain the flatness, the trick is, for 2nd row, work 2 dc in every 2nd ch sp, for 3 row, work 2 dc on every 3rd ch sp and so on..For last row curves - work half dc, dc, half treble, treble, 4-loops, treble, half treble, dc, half dc (one curve completed) - repeat.