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

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.