Laterally related topics: The Neolithic Era, The Stone Builders, The Middle Ages, The Renaissance, The 1600s, The 1800s, The 1700s, The 1400s, The 1500s, The Paleolithic Era, and The 1900s.
The Mathematics and the Liberal Arts pages are intended to be a resource for student research projects and for teachers interested in using the history of mathematics in their courses. Many pages focus on ethnomathematics and in the connections between mathematics and other disciplines. The notes in these pages are intended as much to evoke ideas as to indicate what the books and articles are about. They are not intended as reviews. However, some items have been reviewed in Mathematical Reviews, published by The American Mathematical Society. When the mathematical review (MR) number and reviewer are known to the author of these pages, they are given as part of the bibliographic citation. Subscribing institutions can access the more recent MR reviews online through MathSciNet.
Petruso, Karl M. Additive progression in prehistoric mathematics: a conjecture. Historia Math. 12 (1985), no. 2, 101--106. (Reviewer: Garry J. Tee.) SC: 01A10 (01A15), MR: 86m:01005.
A collection of stone balance weights was recovered from a Late Bronze Age ship (c. 1200 BC) that sank off the coast of southern Turkey (near Cape Gelidonya, modern Finike). Some of these weights are sphendonoid in shape ("approximately the shape of an olive pit"), and appear to be multiples 1, 3, 5, 7, 12, 31, 50, and 54 of a hypothetical unit weight of 9.3 grams (the error is within about 2 percent). There are five weights of 7, and one weight of each of the others. Initially, these balance weights defied analysis, but the author (Petruso) realized that they nearly form a Fibonacci series; he posits the existence of missing weight of 2 and 19. Two problems with this interpretation are the fact that a weight of 7 occurs instead of a weight of 8, and the fact that the weight of 54 does not fit into his system. He suggests that the weight of 8 is a "purposeful and quite utilitarian shift in the basic Fibonacci series .... [to] allow the generation of a 50-unit (rather than 55-unit) mass further along the series." He also notes that the units of 19+31+50 would conveniently add up to 100. As for the 54 unit weight, "it might well have had a specific, idiosyncratic (industrial) purpose which is now lost to us." The author notes that one particular advantage of the Fibonacci-like system is that the accuracy of the individual weights could be quickly checked: for example, one can weigh the 12 against the 5 and the 7. Altogether a fascinating theory, readily readable. Closely related topics: The Balance and the Measurement of Weight, Leonardo of Pisa (Fibonacci), and Archaeology.