Generality and iteration
Interpreting algorithms for squaring and cubing exposed in Śrīdhara’s [Book] of Three Hundred [Verses] (Triśatī) and its commentary
Bibliographic Data
| ID | 22415237 |
|---|---|
| Authors | Taro Tokutake (0000-0002-8118-626X, Centre National de la Recherche Scientifique, corresponding author) |
| Year | 2026 |
| Volume | 75 |
| Pages | 103228 |
| Publication date | 2026-12-01 |
| Open Access | Yes |
| Type | ARTICLE |
| Venue | Historia Mathematica (JOURNAL) |
| Journal identifiers | ISSN: 0315-0860 • E-ISSN: 1090-249X |
| Publisher | Elsevier BV (PUBLISHER) |
| DOI | 10.1016/j.hm.2026.103228 |
| OpenAlex | W7164534284 |
| Language | EN |
| References cited | 1 |
The present paper explores the relationship between generality and iteration in algorithms for squaring and cubing as presented in Śrīdhara’s Sanskrit arithmetic treatise, the [Book] of Three Hundred [Verses] ( Triśatī ), along with its anonymous commentary. I first examine the structure of each algorithm as stated in the base text. I then interpret and reconstruct the procedures based on the descriptions in the commentary. Finally, I explore a substantial difference in the formulation of the two algorithms and propose a hypothesis concerning this difference and Śrīdhara’s practice of generality. The present study suggests that the generality of the algorithms is underscored by the concise expression of their iterative nature. This iterative aspect is articulated through specific keywords and phrases that play a central role within the algorithms.
Generality · Iterative method · Historical Linguistics and Language Studies · History and Theory of Mathematics · Indian and Buddhist Studies
| Highly cited | No |
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