Extending Hridaya Kolam to Multiple Loops: A Study of Non-Coprime Dot--Arm Structures
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914107511275520 |
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| author | Manna, Atanu Chakraborty, Suvra Kanti |
| author_facet | Manna, Atanu Chakraborty, Suvra Kanti |
| contents | This paper extends Hridaya Kolam patterns to cases where the number of dots ($m$) and arms ($n$) are not coprime, i.e., $\gcd(m, n) \ne 1$. Such configurations give rise to multiple disjoint closed loops. We propose a modular-arithmetic-based algorithm to systematically generate such patterns, and illustrative patterns for various non-coprime $(m, n)$ pairs are provided to demonstrate the resulting multi-loop structures. These multi-loop Kolam designs can inspire architectural motifs and ornamental patterns in floor plans, facades, and decorative elements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_18907 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extending Hridaya Kolam to Multiple Loops: A Study of Non-Coprime Dot--Arm Structures Manna, Atanu Chakraborty, Suvra Kanti General Mathematics 00A66, 11A07, 68U05 This paper extends Hridaya Kolam patterns to cases where the number of dots ($m$) and arms ($n$) are not coprime, i.e., $\gcd(m, n) \ne 1$. Such configurations give rise to multiple disjoint closed loops. We propose a modular-arithmetic-based algorithm to systematically generate such patterns, and illustrative patterns for various non-coprime $(m, n)$ pairs are provided to demonstrate the resulting multi-loop structures. These multi-loop Kolam designs can inspire architectural motifs and ornamental patterns in floor plans, facades, and decorative elements. |
| title | Extending Hridaya Kolam to Multiple Loops: A Study of Non-Coprime Dot--Arm Structures |
| topic | General Mathematics 00A66, 11A07, 68U05 |
| url | https://arxiv.org/abs/2510.18907 |