The Process of Constructing a Regular Hexagon in the Near East: From Neolithic Pottery to Euclid’s Elements

Document Type : Original Research Article

Authors

1 Ph.D. Candidate in Prehistoric Archaeology at Tarbiat Modares University

2 Archaeology, Humanities, Shahrekord University

Abstract

A regular hexagon is one of the shapes introduced in Plane Geometry and refers to a hexagon with equal sides wherein the size of each angle is 120 degrees. This geometric shape, which can be quickly drawn today, was constructed over a long period in the millennia BC In the Late Neolithic period in Mesopotamia, the primary geometric shapes, including triangles, quadrilaterals, arcs, and circles, were additionally painted on the surface of pottery ware. Naturally, these shapes had been initially drawn by hand, and the sides of the polygons were not comprised of straight lines, or the circles had not been drawn perfectly. However, in the Chalcolithic age, geometric shapes moved away from handmade forms and approached standard ones. This standardization was not possible without drawing tools. In the meantime, the role of compasses or other objects with a similar use was of utmost importance because drawing a circle with such tools paved the way for drawing regular polygons. In fact, from the Late Neolithic, handmade triangles and arcs in the Near East, the first regular hexagon in the late second or the early first millennium emerged over several thousand years. Constructing this geometric shape with the help of standard circles and arcs has been well documented in the Near Eastern archaeological evidence. On the other hand, regular hexagons have been attributed to the second half of the first millennium in the history of mathematics. Therefore, this study reflected on the construction process of this geometric shape and dated its drawing hundreds of years back.

Keywords

Main Subjects

🔓 © 2022 The Author(s). Published by Tissaphernes Archaeological Research Group, Tehran, Iran. Open Access. This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDeriv- atives License (https://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in any way. The ethical policy of Persica Antiqua is based on the Committee on Publication Ethics (COPE) guidelines and complies with International Committee of Persica Antiqua Editorial Board codes of conduct. Readers, authors, reviewers and editors should follow these ethical policies once working with Persica Antiqua. The ethical policy of Persica Antiqua is liable to determine which of the typical research papers or articles submitted to the journal should be published in the concerned issue. For information on this matter in publishing and ethical guidelines please visit www.publicationethics.org.

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History

  • Receive Date: 06 February 2022
  • Revise Date: 07 March 2022
  • Accept Date: 06 April 2022

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