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中文摘要：
为了用数学形式表征地图比例尺的本质特征,地图比例尺的概念需要精密的数学表达形式。根据地图比例尺与地球制图半径、可视化点对应点元半径的函数关系,给出两个地图比例尺的数学定义;由函数的定义域推出大、中、小地图比例尺的分类;并从拓扑学覆盖的数学定义,论证制图区域多种地图比例尺覆盖的科学合理性。
英文摘要：
In order to express the essential features of map scale in mathematical form,the concept of map scale needs a precise mathematical expression form.According to the relationships between map scale and earth mapping radius as well as visualization point＇s corresponding point element radius,the paper gives two mathematical definitions of the map scale.From the domain of the function it introduces the classification of large,medium and small scale maps.From the mathematical definition of topology coverage,the paper demonstrates the scientific rationality of various map scale coverage in the cartographic region.
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