Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2304.03684

India and the Calculus of Trigonometric Functions

Vijay A. Singh
View original source ↗Read source document ↗Export metadata ↓

Abstract

We discuss the work of a brilliant line of Mathematicians who lived in central Kerala and starting with its founder Madhava (1350 CE) developed what can best be described as Calculus and applied it to a class of trigonometric functions. We explain, with the example of the expansion of the inverse tan function, how they handled integration. Further, they took forward the work of the fifth century mathematician Aryabahata (499 CE), worked with differentials, and developed the expansion of the sine and the cosine functions. The work \textit{Yuktibhasa} (circa 1500 CE) which maybe described as the first textbook on Calculus, also describes in detail the evaluation of the area and volume of trigonometric functions as well as a variety of expansions for $\textit{pi}$. Our treatment is pedagogical and we present exercise problems and invite the enterprising student to try their hands at approximations and integration $\textit{a la}$ the Madhava way.

Explore related subjects

math.HO

Keep this discovery

BibTeXRIS

Vijay A. Singh. 2023-04-07. India and the Calculus of Trigonometric Functions. https://arxiv.org/abs/2304.03684

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Perspectives on the unit distance problem

This is a survey on an old open problem in combinatorics called the unit distance problem, and the field of mathematics around it, called incidence geometry. What do we know about the problem? Why is it difficult? How does it connect with other parts of math?

math.HO↗
arXiv2026

A Categorical Approach to Euclidean Ratios and Proportions

A categorial approach to the non-metric geometry in Books V and VI of Euclid's \textit{Elements} is presented. Specifically, we introduce a diagrammatic syntax that can be overlaid immediately on his diagrams, thus bridging intuitive presentation with fidelity to Euclid's arguments. This syntax makes complicated definitions like V.5, and indeed the arguments throughout books V and VI, including arguments about similar figures, intuitively clear. We show in an appendix that this syntax can be used to solve a puzzle regarding ancient mathematics. Finally, we offer evidence that this approach to Euclidean diagrams is rooted in the Aristotelian tradition itself, and that a similar syntax was utilized, in antiquity, for related questions of numeric and proportions. Thus the syntax is plausibly faithful to Euclid's own thought-world, and not an outside-imposition.

math.HO↗
arXiv2026

Some Early Results by Tutte Regarding the Cycle Double Cover Conjecture in 1948

OpenAI recently announced a proof of the Cycle Double Cover (CDC) Conjecture. Most media reports have characterized it as a 50-year-old open problem. In reality, according to a 1987 letter from Tutte to Fleischner, the Cycle Double Cover Problem has been open for at least 80 years. Two early results regarding the CDC conjecture were established in one of Tutte's 1949 publications.

math.HO↗