此篇論文我們主要是探討熱帶幾何下，凸集(convex set)以及圓錐(cone)的生成元素(generator)個數。在第二章中我們對一些基本環境及運算工具做介紹，例如：熱帶半環(tropical semiring)為度量空間(metric space)、極限值的運算性質等等，在第三章中我們探討回收錐(recession cone)、凸集及圓錐的性質，其中包含三者之間的關係，而在第四章中我們探討閉圓錐(closed cone)、緊緻凸集(compact convex set)、閉凸集(closed convex set)三者的生成元素個數，並以實例說明此性質，最後我們將推論出一個方法來找出在二維的熱帶空間底下的有限生成圓錐之生成元素。 / In this thesis, I will discuss the generators of cone and convex set in tropical geometry. In Chapter 2, basic environment in tropical geometry and arithmetic tools are introduced here, such as how to find the limit value in tropical geometry or deciding if tropical semiring is a metric space, etc. In Chapter 3, I explore the properties of cone, convex and recession cone, inclusive of the relations of one another. In Chapter 4, the generators of a closed cone, a compact convex set, a closed convex set are provided with illustrations to present the properties. It will finally lead to a method to find the generators of the finitely generated cone in two dimesion space.

本篇文章主要研究熱帶幾何之圓錐曲線，即二元二次多項式``根''的圖形。在文章中，我們以二元二次多項式係數關係做曲線的分類，歸納出20種熱帶圓錐曲線圖形，並證明此為完整的熱帶圓錐曲線之分類。然後，我們進一步討論如何調整二元二次多項式係數使圖形平移。最後，提出以熱帶直線輔助熱帶圓錐曲線快速作圖的方式。 / The purpose of the present study is to investigate conics -the graphs of the ``roots'' of quadratic polynomial- in tropical geometry. First, we induct and classify twenty types of tropical conics based on the relation between the coefficients and roots in quadratic polynomial. Second, evidences are provided to prove the classification thorough and intact. Then, we further discuss how to modify the quadratic polynomial in order to translate the graphs. Finally, suggestion about how to use tropical line to assist the graphing of tropical conics more efficiently is provided.