Abstract: What on earth is the size of China’s land area in total? No person can answer this question.Indeed,this paper tries to discuss the scale dependency of geographical area measurement rather than the total area of Chinese land.In theory,a country bordering on oceans can be divided into two parts.The main land can be modeled with Koch’s island,and the islands and islets in the marginal seas can be described with the Pareto distribution.The Koch island model suggests that the boundary line of the land area is a fractal line,while Pareto’s law suggests that the size distribution of islands and islets in an ocean is of scaling invariance.A coastline,consisting of bays and headlands,has irregularity at a certain degree,which was discussed by B.B.Mandelbrot in his fractal works.On the other hand,an archipelago is made up of many islands and islets.Zoom in on a smaller portion and it,in turn,will be composed of smaller islands and islets.The distribution of islands and islets does not change with distance.In technical terms,the archipelago is said to be of self-similarity at different scales,that is,it is a fractal set of random phenomena.
A fractal is based on a form of symmetry with scale invariance under contraction or dilation.The scale invariance is known as dilation symmetry or scaling symmetry.Symmetry implies some kind of immeasurable quantity.Because of scaling symmetry,the length of coastline,the area of a country’s land,and so on,cannot be well and truly measured.Measuring the area of a country from space will give a lower total than measuring it from 100 meters away,because of the extra detail at a larger scale.As the scale gets finer,more details(smaller islands or islets) can be picked up.The inevitable conclusion is that the total area of the country appears to increase indefinitely.This is just the scale-dependency of geographical measurements.The essence of land area is similar to that of the coastline length.The result(area or length) depends on the scale at which you make the measurement.Therefore,the land area data of different sources is not always comparable due to different sizes of yard measure,different scales of digital maps and different resolutions of geographical images.

Key words: scaling symmetry, fractal line, scale dependency, land area, Koch island, Pareto distribution, political geography, China