The law of topography is a law in geography that studies the topographic changes of the earth's surface. One of the most famous is wallenstein's law, that is, the terrain changes tend to be gentle. Mathematically, it can be expressed by the concept of slope, that is, the ratio of elevation change to distance. By calculating the slope or gradient, the degree of terrain fluctuation can be displayed.
Climate law is to study the operation law of climate system. Among them, the Kopec climate classification system is the most famous. The system divides the world into several different climate types according to indicators such as temperature and precipitation. Mathematically, statistical methods can be used to analyze climate data, including mean, standard deviation and correlation coefficient.
Ecological law is the law of studying the species, quantity and relationship of organisms in the ecosystem. Among them, the most important is the neutral ecological law and the relationship between species diversity and area. Neutral ecological law describes the randomness of species occurrence, which can be expressed by probability distribution function. The relationship between species diversity and area shows that species diversity will increase with the increase of observation area. This relationship can be studied by mathematical methods such as curve fitting.
In short, the three laws of geography can be described and explained by mathematical methods and models, although there is no clear mathematical expression. This mathematical description and analysis is helpful for us to deeply understand and study various laws and phenomena in geography.