EJMT Abstract

Fisher-Mellor defined knotwork design as a type of alternating link diagram related to Celtic knots. In this paper, we define Celtic knot design (CKD) induced from $p\times <!--\; \times \; -->q$ square grid and $p\times <!--\; \times \; -->q$ honeycomb grid as a generalized knotwork design. We show the geometric properties of CKDs from these grids and present how these structures can be mathematically described and classified. These concepts and results support mathematics education by deepening understanding of geometric structures and work well with technology-enhanced instructional design. This multidisciplinary approach, integrating mathematics, art, culture, and technology, offers potential applications in STEAM education.