等周不等式主要是說在平面上任意的封閉區域，由固定周長所圍成的面積，其中以圓圍出來的面積為最大。在此論文中我們介紹傳統微分幾何的等周不等式及多邊形的等周問題，接著從Brunn-Minkowski不等式與超平面的概念將等周不等式推廣到d維度。另一方面，介紹Steiner不等式及平行集合的概念來推導相關的等周不等式。 The Isoperimetric inequality says that the area of any region in the plane bounded by a curve of a fixed length can never exceed the area of a circle whose boundary has that length. In this paper, we present isoperimetric inequality of classical differential geometry and polygonal isoperimetric problem. Next, we consider isoperimetric problem in Rd using Brunn-Minkowski inequality and the concept of hyperplanes. On the other hand, we consider isoperimetric inequality of Hadiwger using Steiner's Inequality and the concept of the out t-parallel sets.
