An early Chinese derivation of the volume of a pyramid: Liu Hui, third century A.D.

Wagner, Donald B.

doi:10.1016/0315-0860(79)90076-4

Cited by 48 publications

(5 citation statements)

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“…and the East (for instance, Liu Hui in the third century C.E., Zu Chong-Zhi and his son Zu Geng in the late fifth century C.E.). These examples provide stimulating and instructive didatical material for the classroom (Calinger, 1982(Calinger, /1995Shen, 1997;Siu, 1993;Wagner, 1978Wagner, , 1979. The story on the computation of the volume of a sphere is particularly noteworthy, not only because of the ingenious use of the method of indivisibles to compute the volume of the closely related object ''Mou-he-fang-gai'' (literally, it means ''box with a closely fitted square lid''), which is the common portion of two cylinders of equal diameter placed with axes orthogonal to each other, but also because of the kind of intellectual integrity and humbleness Liu Hui displayed.…”

Section: Era Of Explorationmentioning

confidence: 97%

Proof as a practice of mathematical pursuit in a cultural, socio-political and intellectual context

Siu

2008

ZDM Mathematics Education

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Through examples we explore the practice of mathematical pursuit, in particular on the notion of proof, in a cultural, socio-political and intellectual context. One objective of the discussion is to show how mathematics constitutes a part of human endeavour rather than standing on its own as a technical subject, as it is commonly taught in the classroom. As a ''bonus'', we also look at the pedagogical aspect on ways to enhance understanding of specific topics in the classroom.

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Section: Era Of Explorationmentioning

confidence: 97%

Proof as a practice of mathematical pursuit in a cultural, socio-political and intellectual context

Siu

2008

ZDM Mathematics Education

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“…We shall develop aspects of this practice of proof that are related to the theme of the present paper. For other aspects, the reader is referred to Wagner 1979;Wu Wenjun 1982;Volkov 1992Volkov , 1994Chemla 1991Chemla , 1992Chemla , 1997a. A more exhaustive bibliography can be found in Chemla, Guo forthcoming.…”

Section: Generality Without Abstractionmentioning

confidence: 99%

“…Likewise, more generally, in his commentaries, the solid blocks and figures referred to in order to interpret the meaning of computations and establish the correctness of algorithms seem to have the most particular dimensions, being all regularly equal to small integers. 40 This feature of visual auxiliaries in ancient China 38 For a detailed analysis of the argument, which I cannot repeat here, see Wagner 1979. Chemla (1992 suggests modifying the critical edition of the text in such a way that the reasoning appears as bringing into play the general operation: yi ying bu xu, "Use the excess to fill up the void."…”

Section: The Various Figures Of the Search For Generality In Ancient mentioning

confidence: 99%

Generality above Abstraction: The General Expressed in Terms of the Paradigmatic in Mathematics in Ancient China

Chemla

2003

SIC

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Argument Abstraction is commonly valued as being essential to mathematics or even consubstantial with it. In relation to this belief, mathematical texts from Antiquity-be they from Babylon, Egypt, or China-, which are composed of seemingly concrete problems and algorithms solving them, have been considered to be practice-oriented and deprived of theory. This paper offers an alternative view on both issues. Relying on evidence given by third-century commentaries on The Nine Chapters on Mathematical Procedures, a Chinese treatise composed around the beginning of the Common Era, this paper argues that, in the scholarly mathematical tradition of ancient China, generality was more valued than abstraction. In this respect, problems must be interpreted as paradigms, in the sense grammarians use the term. One of the goals of theoretical endeavor was to exhibit the most general operations possible, and this purpose can be read in quite a few specific features of mathematical practice and concepts. Moreover, it is shown that abstraction is not absent from The Nine Chapters, but that it entertains with generality a relationship that requires analysis and can by no means be taken for granted. These ancient sources hence constitute an invitation to develop a critical approach toward the relation of mathematics to abstraction and generality taken separately, as well as the relation of these two values with each other.

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“…These are primary in application’ (ch. 5; Qian 1963, 168.3–4; Wagner 1979, 182; Lloyd 1996, 161, contrast the slightly different translation in Chemla and Guo 2004, 433).…”

mentioning

confidence: 99%

“…But if it is certainly the case that, compared with the ancient Greeks, the Chinese showed comparatively little interest in conic sections, it has plausibly been argued (e.g. Wagner 1978a, 1979; cf. Netz 2018) that the Chinese arrived at something like the equivalent of Cavalieri's principle by a different route, the investigation of the areas of complex solids.…”

mentioning

confidence: 99%

The problems of exceptionality: The case of Archimedes and the Greeks

Lloyd¹

2022

Interdisciplinary Science Reviews

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The points at which Greek mathematics in general and Archimedes' contributions in particular are exceptional are here assessed by way of a comparison with the extensive evidence from ancient China. While underlining the need for caution concerning the extent to which concrete conclusions are possible, the outcome is broadly to confirm Netz's argument that a key factor in Archimedes' success and influence was the way in which in a social and intellectual environment that favoured debate, he was able to contest an assumption found in both the Platonic and Aristotelian traditions. Where they had imagined a sharp division (albeit differently defined) between what they assigned to 'physics' and to 'mathematics' respectively, Archimedes showed how those two inquiries could be treated as complementary to one another, thereby opening up the possibility of new styles of physical demonstration.

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An early Chinese derivation of the volume of a pyramid: Liu Hui, third century A.D.

Cited by 48 publications

References 1 publication

Proof as a practice of mathematical pursuit in a cultural, socio-political and intellectual context

Proof as a practice of mathematical pursuit in a cultural, socio-political and intellectual context

Generality above Abstraction: The General Expressed in Terms of the Paradigmatic in Mathematics in Ancient China

The problems of exceptionality: The case of Archimedes and the Greeks

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