Other effects can be achieved by using yarns with different colour changes and/or making the rings in equal widths.
It seems counter-intuitive that the same small number of stitches should be added on every round of knitting to make the circle keep growing and to lie flat but that is exactly what happens.
Rope around the world problem
Imagine a piece of string wrapped around the Earth's equator, which is a distance of about 40,000 km. How much string would you need to add to make it sit 15 cm above the surface?
Slightly less than one 1 metre.
It is all to do with proportion. The circumference of a circle is always just a bit more than three times the diameter. Whatever measurement you increase the diameter by you are increasing the circumference by a bit more than three times that.