Category
Applied
Description
Making math tangible and accessible to everyone has always been an ongoing process, and as a part of that process this study aims to take steps forward in the area of square packing. Mathematics can often seem theoretical and aloof, something only for those in their “ivory tower.” Making mathematics into something tangible, something that anyone can see and, more importantly, play with, brings the extensive and invaluable field of mathematics down to an accessible level for everyone to use and enjoy. This study investigates square packing, the problem of deducing the smallest square that can contain a given number of equally sized smaller squares. Square packing has important applications in packaging and shipping and in machining sheets with minimal waste, as well as finding its way into various other niches. Twelve printed square tiles and a set of square frames will be 3D printed for use as a demonstration of the problem. To be investigated are the minimum packing sizes of up to twelve square tiles in the smallest possible frame. The primary focus will be on packing five squares, ten squares, and eleven squares. The minimum frame size for arrangements of five and ten squares are known, but the minimum for eleven squares remains a mathematical mystery to date. These components will let people investigate the problem by hand, seeing how the solution makes sense physically and intuitively. The 3D printed components will bring the study from a theoretical problem on a whiteboard to a tangible, engaging, and, most importantly, accessible problem for anyone to puzzle with, bringing the questions and solutions of modern mathematics into everyday life.
3D Printed Square Packing: Making Math Accessible for Everyone
Applied
Making math tangible and accessible to everyone has always been an ongoing process, and as a part of that process this study aims to take steps forward in the area of square packing. Mathematics can often seem theoretical and aloof, something only for those in their “ivory tower.” Making mathematics into something tangible, something that anyone can see and, more importantly, play with, brings the extensive and invaluable field of mathematics down to an accessible level for everyone to use and enjoy. This study investigates square packing, the problem of deducing the smallest square that can contain a given number of equally sized smaller squares. Square packing has important applications in packaging and shipping and in machining sheets with minimal waste, as well as finding its way into various other niches. Twelve printed square tiles and a set of square frames will be 3D printed for use as a demonstration of the problem. To be investigated are the minimum packing sizes of up to twelve square tiles in the smallest possible frame. The primary focus will be on packing five squares, ten squares, and eleven squares. The minimum frame size for arrangements of five and ten squares are known, but the minimum for eleven squares remains a mathematical mystery to date. These components will let people investigate the problem by hand, seeing how the solution makes sense physically and intuitively. The 3D printed components will bring the study from a theoretical problem on a whiteboard to a tangible, engaging, and, most importantly, accessible problem for anyone to puzzle with, bringing the questions and solutions of modern mathematics into everyday life.
