Archimedes Revisited and Beyond.

In the article "Archimedes Revisited and Beyond," the author explores the physical orientation of floating objects, going beyond traditional understandings of weight and buoyant force. Motivated by an article on iceberg orientations, the author aims to provide theoretical answers to questions about floating object orientation. The paper discusses concepts such as the center of gravity and buoyancy, and presents examples of floating cubes with different densities. The article also mentions previous works on the topic and provides images of the floating cubes. Additionally, the document discusses the concept of the metacenter and its application to the stability of floating objects, specifically cubes. The metacenter is a point that determines the stability of a floating orientation. The document provides equations and examples to calculate the metacenter and determine the stability of a floating cube. It briefly mentions the application of the concept to other shapes, such as cylinders. The author, Terry Toepker, is an Emeritus Professor with extensive teaching experience. [Extracted from the article]