An Eighth Century Chinese Table of Tangents
Abstract
It has been generally held that the first appearance of the tangent function was in the form of the shadow tables used by Moslem astronomers of the ninth century A.D. Suggestions of the use of trigonometrical techniques in eighth-century China have now been verified by the discovery of a table of functions equivalent to a tangent table making use of third-order finite differences. This table, composed by the Buddhist monk I-hsing ドド行 about A.D. 725, was apparently an independent development based on Indian information about the use of sines. It played an important role in I-hsing’s work on mathematical astronomy, and may be connected with certain accusations of plagiarism made shortly after his death.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Some modern scholars and virtually all premodern authors conflated Yixing and pseudo-Yixing, leading to problematic chronologies of Yixing's life and activities.
“Some modern scholars and virtually all premodern authors have conflated these two figures.This has led to problematic chronologies of Yixing's life and his activities.5”
From The Astronomical Innovations of Monk Yixing 一行 (673–727) (2022) · cites this paper as [5]
Cited by
Sorted by citations
The Astronomical Innovations of Monk Yixing 一行 (673–727)
Kotyk, J. (2022) · Religions · doi:10.3390/rel13060543 · Cited by 2 · see citing works
- Authors
- Cullen, C.
- Corresponding author
- Cullen, Christopher
- ORCID
- Cullen, Christopher
- Venue
- East Asian Science, Technology, and Medicine
- Publisher
- Walter de Gruyter GmbH
- Published
- 1982-06-25
- Volume
- 5
- Issue
- 1
- Pages
- 1-33
- ISSN
- 1562-918X (ISSN-L)
- 2666-9323
- OpenAlex
- W2201564264
- Cited by
- 11
- References
- 0
- Citations by year
- 2025: 1 · 2024: 1 · 2015: 2
- FWCI
- 0.00
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- East Asian Science Technology and Medicine (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Historical Astronomy and Related Studies
- Physical Sciences › Mathematics › Theoretical Computer Science › History and Theory of Mathematics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › History and Developments in Astronomy
- Keywords
- tangent function, tangent tables, Chinese mathematics, 8th century, mathematical astronomy, Buddhist monks, plagiarism allegations, history of trigonometry
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
