Isoperimetric Problems on n-sided Prisms
Amrizal Marwan Ali (a*), Denny Ivanal Hakim (b)

a) Mathematics for Teaching Study Program, Institut Teknologi Bandung, Bandung, Indonesia
*amrizalmarwanali[at]gmail.com
b) Analysis & Geometry Research Division, Institut Teknologi Bandung, Bandung, Indonesia

Abstract

In two-dimensional figure, the isoperimetric problem refers to finding two-dimensional figure that will produce the largest area among several shapes with equal perimeter. This research extends the isoperimetric problem to finding three-dimensional shapes with maximum volume among those having equal surface area. The study aims to solve the isoperimetric problem for prisms with regular n-sided base, prisms with irregular n-sided base and cylinder. In this research, the discussion is limited to prisms with irregular and irregular bases. The problem of finding the smallest surface area of a given three-dimensional figure with the same volume. The method used is geometric proof. we will see the relationship between isoperimetric problems in two dimensional figures and isoperimetric problems in three-dimensional figure. Obtained the results of the isoperimetric problem from two prisms with regular n-sided bases and a prism with regular m-sided bases with n \(\leq \)m, two prisms with regular n-sided bases and a prism with circular bases (cylinder), and two prisms with regular n-sided bases and a prism with irregular n-sided bases.

Keywords: Isoperimetric Problem- Prisms- Volume- Surface Area

Topic: Minisymposia Geometry and Topology