Monte Carlo methods are non-parametric algorithms that use random numbers and theorems of probability theory to approximate values that are not random. The purpose of my research was to approximate the surface of different geographical areas that can be easily approximated to polygons (e.g. lakes, glaciers, deserts) with Monte Carlo simulations starting from either Cartesian coordinates or pictures. Computer science would not exist without math, and this research project showed me the importance of a deep understanding of probability theory in the world of simulations and, more generally, the importance of developing new theorems and algorithms. The results of my research could be developed in different ways: it would be interesting to produce software that allows one to approximate areas from pictures taken from a smartphone; as well, the theorem I found has to be proven, and also Monte Carlo methods as a means of random number generation can always be improved. There are still many possibilities.
「為配合國家發展委員會「推動ODF-CNS15251為政府為文件標準格式實施計畫」，以及 提供使用者有文書軟體選擇的權利，本館檔案下載部分文件將公布ODF開放文件格式， 免費開源軟體可至LibreOffice 下載安裝使用，或依貴慣用的軟體開啟文件。」