Papers by Duncan J Melville
Proceedings of the London Mathematical Society, 1997
Algebr Represent Theory, 1998
Revue d Histoire des Mathematiques, 2005
Il y avait en Mesopotamie un procede standard pour resoudre des problemes quadratiques impliquant... more Il y avait en Mesopotamie un procede standard pour resoudre des problemes quadratiques impliquant des longueurs et des surfaces de carres. Nous montrons, sur un exemple de Suse, que des constantes geometriques ont ete employees pour ramener des problemes concernant d'autres figures au format standard.
The Encyclopedia of Ancient History, 2012
In: Computations and Computing Devices in Mathematics Education Before the Advent of Electronic Calculators, Alexei Volkov and Viktor Freiman, eds., 2018
The history of Mesopotamian mathematics begins around 3300 BCE with the development of written sy... more The history of Mesopotamian mathematics begins around 3300 BCE with the development of written systems for recording the control and flow of goods and other economic resources such as land. Numeration was bound up with measurement and was a collection of concrete systems. One of the key developments over the subsequent thousand years or so was the gradual rationalization of these complex concrete systems and the consequent emergence of an abstract conception of number and techniques of computation that applied regardless of metrological category. Throughout their history Mesopotamian scribes organized knowledge in the form of lists. In mathematics there were also lists, but along with lists came metrological and mathematical tables, two-dimensional arrays of data that organized information both vertically and horizontally. A key example is tables giving lists of lengths of sides of square or rectangular fields, along with their areas; the problem of computation of areas remained a constant concern throughout the period covered here. In this chapter, we cover the development of Mesopotamian computation from the archaic period up to the edge of the emergence of the fully abstract sexagesimal computational system for which they are renowned, tracing, as far as can be seen with currently available sources, the long developmental process.
CMS Notes, 2017
On Old Babylonian mathematical education.
In the early eighteenth-century, techniques of computation for decimal fractions, especially non-... more In the early eighteenth-century, techniques of computation for decimal fractions, especially non-terminating decimals, were being developed amid a debate over their utility compared to common fractions for merchants and tradesmen facing complicated metrological and currency systems. The most comprehensive exploration of these techniques was undertaken by John Marsh in his Decimal Arithmetic Made Perfect of 1742. In this paper we explain Marsh's achievement, locate his contribution in the context of earlier work, and consider his audience and its implications as evidence for the depth and spread of interest in mathematics in England
Reciprocals play a signiflcant role in Mesopotamian mathematics since divi- sion is performed as ... more Reciprocals play a signiflcant role in Mesopotamian mathematics since divi- sion is performed as 'multiplication by the reciprocal'. An important skill for a Mesopotamian scribe was the ability to flnd reciprocals, and there are a number of algorithms for achieving this. The product of a number and its reciprocal is 1. For any number n, we let n denote the reciprocal. Then nn = 1. In Mesopotamia, the notion of the 'reciprocal' only appears after the introduction of the abstract sexagesimal system, which utilizes a relative place value. No absolute scale of the numbers is indicated and so, in efiect, we treat as a number and its reciprocal any pair of numbers whose product is a power of 60, and hence denoted by 1 in the
In H. Neumann, et al, es. Krieg und Frieden im Alten Vorderasien. RAI 52. AOAT 401. Munster, 517-526., 2014
We survey recent developments and new directions in Mesopotamian mathematics over roughly the las... more We survey recent developments and new directions in Mesopotamian mathematics over roughly the last decade.
These are brief, informal, uncorrected notes to accompany my talk at the Joint Math Meetings in San Antonio, Sunday, January 11, 2015. A more developed preprint will be forthcoming. Comments and corrections are welcome.
Proceedings of the Canadian Society for the History and Philosophy of Mathematics, 2005
From the Banks of the Euphrates (Fs. Slotsky), 2008
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Papers by Duncan J Melville
These are brief, informal, uncorrected notes to accompany my talk at the Joint Math Meetings in San Antonio, Sunday, January 11, 2015. A more developed preprint will be forthcoming. Comments and corrections are welcome.
These are brief, informal, uncorrected notes to accompany my talk at the Joint Math Meetings in San Antonio, Sunday, January 11, 2015. A more developed preprint will be forthcoming. Comments and corrections are welcome.
Canton, NY 13617. The Role of Third Millennium Metrology in the Development of the
Mesopotamian Sexagesimal Place-Value System. Preliminary report.
Some recently published metrological tables from the second half of the third millennium indicate a systematic exploration
of linkages between length and area metrologies. The extension into small units was something the prevailing metrological
systems were particularly ill-equipped to handle. The response was a development of sexagesimally-based sub-units. In
this paper we argue that these sexagesimal explorations indicate a stage in the development of sexagesimal numeration
towards a fractional and, ultimately, place-value system. (Received January 17, 2015)
Canton, NY 13617. New Directions in Mesopotamian Mathematics.
We will give a brief survey of the current state of knowledge of Mesopotamian mathematics and a summary of recent
directions and developments in research. We will highlight some of the most interesting new questions and methodologies
including close analysis of shape and size of tablets, increased sensitivity to regional variations in mathematical practice,
and development in cross-cultural studies. (Received September 13, 2014)
surveying, was driven by measurements of ever-increasing exactness.
The mathematical instrument makers who designed and refined instruments of exquisite precision had to be experts in both theory and practice. In this talk I will explain some of the
problems faced, and techniques used, by the leading practitioners of the day to produce such accurate measurements.
Social network analysis emphasizes the importance of nodes of high degree (individuals with many connections, in this context), especially those acting as bridges. I argue that Kirby performs this role for Gainsborough, providing connections to several key Suffolk cliques (subgroups with many internal ties).