Recursive Knowledge Procedures Informing the Design of the Parthenon : One Instance of Continuity between Greek and Near Eastern Mathematical Practices

Lehman, Geoff; Weinman, Michael

doi:10.1515/9783110565959-009

Cited by 2 publications

(3 citation statements)

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“…The Greeks therefore asked important philosophical questions when they did their higher mathematics. The Golden Mean provoked much discussion of number theory since the ratio (1 to approximately 1.6) could not be expressed in a whole number (Lehman and Weinman, 2018).…”

Section: Ancient Greek Mathematicsmentioning

confidence: 99%

Was seventeenth-century British political arithmetic a precursor of nineteenth-century economic science?

Taylor

2023

Terra Econ.

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The 19th-century English economist W.S.Jevons revisited the work of Gregory King. A seventeenth-century follower of Sir Francis Bacon, King had described in a brief empirical observation how price correlated with supply. The history of seventeenth-century commercial mathematics, this essay suggests, provides essential background for understanding the empirical observation which Jevons received from King. The 17th century was the pivot time during which new techniques appeared in higher mathematics, calculus and mathematical probability among them. Higher mathematics incorporated innovations which had previously appeared in commercial mathematics, Arabic numerals, pen and paper calculations, new notations, etc. At the same time, ancient Greek higher mathematics continued for a while, and Gregory King also borrowed some calculations from James Ussher who used ancient Greek higher mathematics. King learned Bacon's empirical method from John Graunt and Sir William Petty, and all three represented a stage of political arithmetic which was midway between Bacon's simple empiricism on the one hand and later mathematical probability and random sampling on the other hand. In this midway stage, statesmen made policy while taking care to obtain data from professional advisors whom they employed. The advisors based their advice at first on a combination of observation, skill, and intuition, but then later they added commercial arithmetic.

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Section: Ancient Greek Mathematicsmentioning

confidence: 99%

Was seventeenth-century British political arithmetic a precursor of nineteenth-century economic science?

Taylor

2023

Terra Econ.

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“…Similar ratios are also found in ancient buildings in other parts of the world. One example is from ancient Greek architecture is the Parthenon, which was constructed using the ratio 4:9 in several aspects ( Penprase 2017; Lehman and Weinman 2018; Shear 2016; Barbara 2005), and another example is the Temple of Hera Lacinia (Marconi 2016; Woodward 2013). The Apollo Temple at Sicyon has a plan dimension in the ratio of 4:13 approximately (Woodward 2013).…”

Section: Introductionmentioning

confidence: 99%

“…The ratio of the column height to the peristyle width of the facade of the unfinished temple at Segesta is in the ratio 4:9, even though its plan dimensions are not in this ratio (Jones 2001). The ratio of diameter to the interaxial length between the columns is also in the ratio of 4:9 (Shear 2016; Lehman and Weinman 2018; Jones 2001). For a length of 9 units, a column of 4 units diameter is provided for a width to height ratio of 4:9.…”

Section: Introductionmentioning

confidence: 99%

Aspects of proportions in Indian traditional domestic architecture

Dhileep¹,

Ramya²,

Kurian³

2021

Interdisciplinary Science Reviews

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Indian traditional architectural practice 'Vastusastra' (Vāstuśāstra) recommends some particular ratios as auspicious for the proportioning of domestic buildings. Similar ratios are found in some ancient buildings belonging to the classical ages in other parts of the world. Recent studies conducted by Dhileep, Kottuppillil, and Kurian [2019. "Orientation and Proportion in Indian Traditional Domestic Architecture." Interdisciplinary Science Reviews 44 (1): 97-109], show that the square and the rectangle formed by the basic auspicious ratio (breadth:length) are geometrically related to a circle with a diameter equal to the length of the rectangle. The mathematical aspects behind these geometrical relationships and other ratio groups given in 'Vastusastra' (Vāstuśāstra) are investigated in this paper. The study reveals that the auspicious ratios help to convert the area of a circle to a rectangle and vice versa, without any loss in accuracy, while using the methods of their age. The traditional social practices are incorporated into these ratios and are modified adequately to fit into the traditional engineering practice.

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Recursive Knowledge Procedures Informing the Design of the Parthenon : One Instance of Continuity between Greek and Near Eastern Mathematical Practices

Cited by 2 publications

References 0 publications

Was seventeenth-century British political arithmetic a precursor of nineteenth-century economic science?

Was seventeenth-century British political arithmetic a precursor of nineteenth-century economic science?

Aspects of proportions in Indian traditional domestic architecture

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