THE MOVING SOFA PROBLEM

• Main Author: Gumilang, Aji
• Format: Final Project
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/65408
• Institution: Institut Teknologi Bandung

There are many problems in the mathematics that until now have not found a solution, one of which is the Moving Sofa Problem. The problem of moving sofas was first proposed by Leo Moser in 1966. The question is to find the shape of largest area in the plane that can be moved through right-angled corner in a twodimensional hallway of width 1. Significant results for solving this problem were first carried out by John Hammersley in 1968. The construction of the Hammersley Sofa is quite simple, where the semicircle is divided into two equal parts, then a rectangle is inserted with a semicircular hole at the bottom of rectangle which has a diameter equal to the length of the rectangle. The next significant result was found by Joseph Gerver in 1992 which became known as the Gerver Sofa and is still the largest today. The first thing to do in this research is to analyze the movement mechanism of the sofa through the corridor start from simple shape. From the previous results, then finding the relationship between simple-shaped sofas and the Hammersley Sofa, and analyze the mechanism of the Hammersley Sofa so that it can pass through the corridor. Finally, there is a discussion about the characterization of the moving sofa problem solution. The main results obtained include a square sofa with a length of 1 being the largest sofa that can pass through the corridor with translational motion, a semicircular sofa with radius 1 being the largest sofa that can pass through the corridor with a rotational motion, the Hammersley Sofa is proven to be able to pass through the corridor, a semicircular sofa of radius 1 can be tested to pass through the corridor by characterization of the moving sofa problem solution.