How Much String to String a Cardioid?
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| Title: | How Much String to String a Cardioid? |
|---|---|
| Authors: | David Richeson |
| Source: | The American Mathematical Monthly. 132:807-812 |
| Publication Status: | Preprint |
| Publisher Information: | Informa UK Limited, 2025. |
| Publication Year: | 2025 |
| Subject Terms: | Mathematics - Number Theory, Mathematics - History and Overview, History and Overview (math.HO), FOS: Mathematics, Number Theory (math.NT), 51M25, 51M04, 11A07, 20K01, 20K27 |
| Description: | A residue design is an artistic geometric construction in which we have $n$ equally-spaced points on a circle numbered 0 through $n-1$ and we join with a line segment each point $k$ to $ak$ modulo $n$ for some fixed $a\ge 2.$ The envelopes of these lines are epicycloids, like cardioids. In this note, we prove that the sum of the lengths of these line segments has a surprisingly simple closed form. In particular, if one wants to make one of these designs with string, it is easy to calculate how much string is required. 8 pages, 3 figures |
| Document Type: | Article |
| Language: | English |
| ISSN: | 1930-0972 0002-9890 |
| DOI: | 10.1080/00029890.2025.2529768 |
| DOI: | 10.48550/arxiv.2311.15101 |
| Access URL: | http://arxiv.org/abs/2311.15101 |
| Rights: | arXiv Non-Exclusive Distribution |
| Accession Number: | edsair.doi.dedup.....81bbbbf1a0912d7af4b80c12fb3718b5 |
| Database: | OpenAIRE |
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Nájsť tento článok vo Web of Science | Abstract: | A residue design is an artistic geometric construction in which we have $n$ equally-spaced points on a circle numbered 0 through $n-1$ and we join with a line segment each point $k$ to $ak$ modulo $n$ for some fixed $a\ge 2.$ The envelopes of these lines are epicycloids, like cardioids. In this note, we prove that the sum of the lengths of these line segments has a surprisingly simple closed form. In particular, if one wants to make one of these designs with string, it is easy to calculate how much string is required.<br />8 pages, 3 figures |
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| ISSN: | 19300972 00029890 |
| DOI: | 10.1080/00029890.2025.2529768 |