Circular knotworks consisting of pattern no. 295: a mathematical approach

Abstract

In Easter Ross in Scotland, there are a number of cross-slabs with various carvings of knotworks. This article deals with a specific circular knotwork on two of the stones originally found there, the Hilton of Cadboll and the Nigg stone. The knotworks are referred to as No. 791 and No. 792 respectively by J. Romilly Allen and Joseph Anderson in their book The Early Christian Monuments of Scotland. Both stones show recurring loops, referred to as pattern No. 295 by Allen and Anderson. This article will consider circular knotworks that can be created with pattern No. 295. We present a mathematical model for this circular knotwork and variations of it. Three parameters are used to characterize the knotwork: the number of circular layers, the number of loops in the innermost layer and finally, a parameter that specifies how the loops are interwoven in the innermost layer. We derive equations to calculate the number of strands for different parameters of the knotwork. The relationships derived involve the greatest common divisor function.

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 8 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.