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 1900s, and The Late Bronze Age.
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.
Jablan, Slavik. Geometry in the pre-scientific period. Geometry in the pre-scientific period; ornament today, 1--32, Hist. Math. Mech. Sci., 3, Math. Inst., Belgrade, 1989. SC: 01A10, MR: 91i:01004.
Discusses geometric ornamentation in Paleolithic and neolithic mathematics, focusing on the symmetries in the ornamentation. The author gives many examples. The only possible symmetry groups of the rosettes are Cn and Dn. There are infinitely many of these, of course, but the basic types occur in both the Paleolithic and the Neolithic. There is a somewhat wider variety in the Neolithic. In addition, neolithic artists have also explored some of the corresponding antisymmetry (or bichromatic) groups. It turns out that all 7 of the frieze already occur in the art of the Paleolithic; thus not surprisingly they occur in the art of the Neolithic as well. The examples show that there are interesting differences in the ways that the frieze patterns are applied. 14 of the 17 bichromatic strip patterns (antisymmetry groups) occur in neolithic ornamental art. 14 of the 17 plane patterns occur in the Neolithic. The author discusses reasons why the artists may have explored the patterns that they did. The author also finds 23 of the bichromatic plane patterns, and gives an example of each. (He classifies these using the Coxeter group/subgroup notation.) Closely related topics: The Neolithic Era, Frieze Patterns, Plane Patterns, Bichromatic Strip Patterns, Bichromatic Plane Patterns, and Rotational Symmetry Groups (Rosettes).
Toth, Nicholas. The prehistoric roots of a human concept of symmetry. Symmetry in a kaleidoscope, 3. Symmetry Cult. Sci. 1 (1990), no. 3, 257--281. (Reviewer: J. S. Joel.) SC: 01A10 (00A99), MR: 93g:01005.
The author discusses how concepts of symmetry occur in Paleolithic artifacts such as stone tools and "Venus" figurines, and also in the roughly circular areas such as those used in a hut or even perhaps at Olduvai site DK 1 (some million years ago). The author has also noted some asymmetries in the making of flaked stone tools. "This slight but statistically significant patterning of asymmetry and possible preferential right-handedness between 1.9 and 1.5 million years ago may indicate a more profound specialization (lateralization) of the left and right hemispheres of the hominid brain by the early stone age." Closely related topics: Symmetry, Archaeology, and Biology.