Exploring Liu Hui’s Cube Puzzle: From Paper Folding to 3-D Design

Overview

Liu Hui was a third century Chinese mathematician widely known for his ingenious commentaries on the Nine Chapters on the Mathematical Art, a summary of ancient Chinese mathematics that became the foundation of traditional Chinese mathematics.  His approach to cube dissection served as the basis of a classic puzzle referred to as "Liu Hui's Cube Puzzle" in this article. The cube is dissected into three solids that are one half, one third, and one sixth of its original volume. The distinctive structure of the cube puzzle allows students to explore its appealing mathematics in pedagogically flexible ways. From paper folding to 3-D modeling, design, and printing, Liu Hui's Cube Puzzle sustains students' mathematical curiosity as they come to appreciate the convergence of a classic puzzle and modern modeling technologies in supporting mathematical thinking.