Archaeoastronomy and Ancient Technologies 2020, 8(1), 47-59
DOI: 10.24411/2310-2144-2020-00006
To the question of the method of calculating the volume of amphoras
Vodolazhskaya, L.N.
Southern Federal University (SFU), Rostov-on-Don, Russian Federation;
e-mails: larisavodol@aaatec.org, larisavodol@gmail.com
Abstract
The article describes the methods for calculating the volume of amphoras used by modern archaeologists, and proposes a new fairly accurate method for calculating the volume of antique sharp-pointed amphoras using the example of narrow-necked light-clay amphoras of the 3rd century AD. option D from Tanais. The method described in the article is based on the mathematical model of amphoras as complex bodies of revolution, and uses the geometric approximation method to create it. Using the developed model, formulas were obtained for calculating the volume of the capacitive part of the amphora and its main segments. The creation of an effective mathematical model for narrow-necked light clay amphoras proves the fundamental possibility of creating similar mathematical models for other types of amphoras, including vessels of large sizes, for example, Pythos. The article gives interpretations of Heron's formulas for "pythoid" and "spheroidal pythos" from the point of view of simple bodies of revolution formed by second-order lines (parabola and ellipse), defines the form of "pythoid" as a truncated paraboloid of revolution, and also concludes that it belongs to Archimedes authorship of "Heron's formulas" for calculating the volume of "pythoid" and "spheroid pythos".
Keywords: amphoras, volume, ellipse, parabola, geometric approximation, Heron, Archimedes, Tanais, narrow-necked light-clay Heraclean amphoras, antiquity
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