Introducing Geometry with a Neolithic Tool Kit

Stephen Luecking

School of Computer Science, Telecommunications and Information Systems

DePaul University, 243 South Wabash, Chicago, IL 60604 USA

E-mail: sluecking@cs.depaul.edu

Abstract

Drawing on his own early experiences as a surveyor the author presents an introduction to the principles and methods of ancient rope pulling, i.e., surveying geometry. Concentrating on some likely field techniques dating back to Neolithic monument builders, this paper assesses similarities and contrasts between the focus of classic geometry on axiomatic proofs and compass and straightedge construction and the propensity of rope pulling toward canonical principles of mensuration and mechanical construction. Included, too, is a comparison of ritualistic and surveying applications of rope pulling, as well as numerous illustrations by the author. Presenting such basic geometric problems as pulling perpendiculars and parallels, working with congruent and right triangles and creating arcs and tangents, the author offers techniques for classroom demonstrations to capture student engagement in geometric ideas.

The origins of geometry lay in demarcating and measuring the earth and the earliest known tools to this purpose were calibrated ropes and plumbed lines. Though the rigors of axiomatic logic that mark geometry as a mathematical field did not come about until 5000 years after the likely beginnings of geometric problem solving by Neolithic priests and builders, the rope pullers art evinces its own remarkable rigor in understanding and using fundamental principles of geometry. Much of this paper delves into some of the likely methods for putting such principles into practice. 

Some of this practice (and the genesis for this paper) comprises the first session of a geometry course in which the instructor takes students through a series of exercises using knotted jute cords and hefty river pebbles. Informed that they have in their possession the entire tool kit for the earliest building engineers, students are guided through basic problems such as those offered below. The goal of this opening class is to instill a respect for geometry as a tool for shaping space, as

Historical Background

Appreciation of a field is invariably enhanced by an understanding of its beginnings and along with that understanding comes a profound respect for the progenitors of that field – for the minds that met and mastered its most basic problems and principles. This is especially true of the origins of geometry. Unlike the stone tools for which the Neolithic age is named, geometry exists only in the patterns inhering in the building projects to which it was applied. The layout tools of these ancient engineers were fashioned from fiber and wood and have long ago decayed. The most important of these was the rope, actually a heavy cord, used to demarcate and extend borders and alignments.

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