The simpler definition is given by the following. To an observer "X" riding on the edge of the rotating disk, the effects of high-speed motion are still in place. So, if "X" were to crawl along the circumference with a ruler and measure the circumference, his ruler will be shortened (due to the Lorentz contraction) and he will have to lay out his ruler "more times" to measure the circumference. Therefore, he will measure the circumference to be "greater" than he would measure it to be if the disk were stationary.