To expand search, see Art. Laterally related topics: Symmetry, Perspective, Fractals in Art, Weaving, Renaissance Art, Basket Making, Tattoos, Pottery, Pattern, Architecture, Proportion and the Golden Ratio, Metal Work, Knots and Knotwork, Bronzework, Needlework, Art History, Origami, and Mazes.
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.
Crowe, Donald W. The geometry of African art. I. Bakuba art. J. Geometry 1 (1971), 169--182. (Reviewer: M. P. Closs.) SC: 01A15 (20H15), MR: 58 #9986a.
Discusses strip and plane patterns occurring in Bakuba art, particularly in textiles and woodcarving. The inspiration for many of these patterns seems to be from weaving, but at least one pattern may originate in the technique of sewing together triangles to make bark cloth. All seven strip patterns occur, and 12 of the 17 possible plane patterns. Discusses the relative proportions of some of these patterns, and gives an example of each. In all but one of the strip patterns, the author gives both cloth and carved examples (the other is given in cloth only, being rare in wood). The author includes an appealing claim about one of the patterns, made by an earlier researcher (too enthusiastic in the view of the authors): "it is probably the most remarkable example of this kind... its discovery is certainly a mathematical accomplishment of the first magnitude." Also see the erratum, Crowe, Donald W., Erratum to: "The geometry of African art. Closely related topics: The Bakuba of Zaire, Frieze Patterns, Plane Patterns, and Weaving.
Knight, Gordon. The geometry of Maori art---Rafter Patterns. New Zealand Math. Mag. 21 (1984), no. 2, 36--40.
The Maori have been fond of carving patterns on their rafters. The author wondered if all seven possible strip or frieze patterns occur in the work of the early Maori, and he found in fact that they do. There is also a brief discussion of the seven types of strip patterns and a flowchart for recognizing them. The author's source was the book Maori Art by A. Hamilton (N.Z. Institute, Wellington, 1901), which is now reprinted by Holland Press, London, 1972. Hamilton's book illustrates 29 rafter patterns, and these turned out to have had only six of the seven patterns; fortunately the one with only vertical reflections turned out in a photograph elsewhere in the book, in "part of the porch of a large house of the Ngati-Porou at Wai-o-Matatini". The author lists two questions that he does not have answers to: What was the relative frequency of each group, and did this vary from one tribal region to another? Also, is there a geometrical difference in character between the early Maori patterns and those produced after the influence of the Pakeha? Closely related topics: The Maori and Frieze Patterns.
Knight, Gordon. The geometry of Maori art---spirals. New Zealand Math. Mag. 22 (1985), no. 1, 4--7. (Reviewer: H. S. M. Coxeter.) SC: 51N20 (01A10), MR: 87m:51060.
The Maoris frequently use spirals in their tattoos and wood carvings. These appear very much like the spirals of Archimedes, but often interlace two or more such spirals. Although the easiest way to construct a spiral similar to the spiral of Archimedes may be to use sets of concentric semicircles (or other segments of circles) offset with respect to one another, the author believes that the Maoris didn't use this technique. "In Spirals of Archimedes, and, it seems, in Maori spirals, there is a gradual, rather than an abrupt, change in curvature." The author gives several examples from Maori artwork; there are examples with 2, 3, and 4 interlaced spirals. The author notes that the 3 spiral form is more common in tattooing patterns than in carving. Apparently there was once a 6 spiral pattern on one of the figures guarding the gateway of Papawai Pa. The center of the spiral can be varied somewhat; for example, two spirals can come together in an S-curve. In one case, "the plain ridges, which form an S-curve, are made to cross over the notched spirals, giving a woven effect. According to Phillips this was chiefly an Arawa modification." The author concludes with a note that the spiral of Archimedes should perhaps have a Maori name instead. He suggests that an investigation of these spirals might be useful in mathematics education (when polar coordinates are studied). Closely related topics: Spirals, The Maori, Tattoos, Archimedes, and Education.