Ethnomathematics Digital Library (EDL)

Browse Results

Subject: Geometry and Topology>Plane Geometry>Patterns (Plane Geometry)

Sort by:
	Title Date current to earliest Date earliest to current

Click on the URL to view the document and on the title to view the complete index entry.

Page 1 of 2

1 2

Previous Next

13 Records

Exploring plaited plane patterns among the Tonga in Inhambane (Mozambique)
by Paulus Gerdes (2001)
[http://www.ethnomath.org/resources/gerdes2001b.pdf]
This study focuses on the plaited plane patterns that are evident in the twill-plaited baskets made by Tonga weavers in the coastal Inhambane province in southeast Mozambique. Quality baskets made by Tonga artisans are highly appreciated for their beauty and utility. Hundreds of various strip patterns are known to have been cataloged. Creative Tonga weavers appear to be inventing new plane patterns. “In general, two plane patterns are considered instances of the same plane pattern if one can be transformed into the other by a (sequence of) rotation(s), translation(s), and/or reflection(s).” This report covers an interesting series of recently created plane patterns. “The invention of the plane patterns responds…to the intellectual, geometric and artistic pursuit of their creator(s), attracting the natural attention of other mathematicians.” Other terms: gipatsi, strip patterns, axial symmetry. (Includes 5 references)
Subject: Applied Mathematics>Mathematics for Humanities>Decorative Arts and Design>Weaving,
Geometry and Topology>Plane Geometry>Patterns>Symmetry,
Geometry and Topology>Plane Geometry>Patterns (Plane Geometry),
Instructional Issues>Educational Research
Geographical area: Mozambique
Cultural group: Mozambican

Finding Meaning in Maths: an introductory program for Aboriginal children
by Beth Graham
[http://www.aiatsis.gov.au/lbry/dig_prgm/e_access/serial/m0036535_v_a.pdf]
Subject: Applied Mathematics>Mathematical Sociology>Kinship Relationships,
Cultural Context>Cultural Perspectives on Mathematics>Euro-centrism,
Cultural Context>Cultural Awareness,
Cultural Context>Influence of Culture on Learning Mathematics,
Cultural Context>Influence of Culture on Teaching Mathematics,
Geometry and Topology>Plane Geometry>Measurement (Plane Geometry),
Geometry and Topology>Plane Geometry>Patterns (Plane Geometry),
Instructional Issues>Curriculum Design,
Instructional Issues>Spatial Ability,
Numbers and Computation>Measurement>Time,
Numbers and Computation>Number Concepts>Natural Numbers>Counting

Frieze designs in indigenous art
by Judi McDonald
[http://mathcentral.uregina.ca/RR/database/RR.09.01/mcdonald1/]
This study describes the seven frieze designs, which are border patterns or designs commonly seen on pottery, wallpaper borders, buildings, and so forth. Symmetry and repetition are their essential elements. “Frieze patterns can be classified mathematically by the types of symmetries they possess, and this classification gives rise to seven symmetry classes.” Included are photographs that show samples of frieze patterns in North America’s indigenous arts and crafts, as well as diagrams, charts, and activities for elementary and secondary school students. Other terms: isometries. (Includes 10 references)
Subject: Applied Mathematics>Mathematics for Humanities>Decorative Arts and Design>Embroidery,
Geometry and Topology>Plane Geometry>Patterns>Geometric Patterns,
Geometry and Topology>Plane Geometry>Patterns (Plane Geometry),
Instructional Issues>Educational Research,
Instructional Issues>Instructional Materials
Geographical area: North America
Cultural group: Native American (United States)

From Liki-designs to cycle matrices: the discovery of attractive new symmetries
by Paulus Gerdes (2002)
[http://members.tripod.com/vismath7/gerd/]
This article presents an overview of how experimentation with Liki-designs led to the discovery of cycle matrices. Eight theorems are presented along with illustrations. The two cycle structures may be considered a new type of symmetry for square matrices. (Includes 14 references)
Subject: Applied Mathematics>Mathematics for Humanities>Decorative Arts and Design,
Geometry and Topology>Plane Geometry>Patterns>Geometric Patterns,
Geometry and Topology>Plane Geometry>Patterns>Symmetry,
Geometry and Topology>Plane Geometry>Patterns (Plane Geometry)

Have you seen (ISGEm Newsletter, Volume 11, Number 1, December 1995)
(1995)
[http://www.ethnomath.org/resources/ISGEm/080.htm]
This annotated bibliography covers four works related to ethnomathematics. Paulus Gerdes examines Pythagorean geometry topics found in African culture in one book, and describes African ethnomathematical research about mathematics education, geometrical thinking and the anthropology of mathematics, and the history of mathematics south of the Sahara in a report. Leslie Villalobos encourages the study of mathematics using problem situations such as sustainable agriculture. Claudia Zaslavsky describes how a multicultural perspective in an elementary and middle grade math curriculum can enrich all students’ learning. She suggests focusing on problem solving and extending learning to issues within local communities. Other terms: Bakuba, Egyptian, magic squares, limits, area, Angolan sand drawings, symmetry, triangles, pattern, weaving, anthropology, education, technology, art, games.
Subject: Cultural Context>Influence of Culture on Teaching Mathematics>Culturally-based Instruction,
Cultural Context>Cultural Awareness,
Cultural Context>Cultural Perspectives on Mathematics,
Cultural Context>Influence of Culture on Learning Mathematics,
Geometry and Topology>Plane Geometry>Triangles>Pythagorean Theorem,
Geometry and Topology>Plane Geometry>Patterns (Plane Geometry),
Mathematics History
Geographical area: Sahara (Africa)

Japanese Mathematics Museum
[http://mathmuse.sci.ibaraki.ac.jp/indexE.html]
This website provides links to different areas of the mathematics museum. The descriptions are in Japanese and English. Examples of the rooms include a fractal 3D gallery, a journey to Wasan, Sangaku, and a Japanese temple geometry problem. Other links are provided to related online museums of the world. Other terms: symmetry, tellastions, Barth sextic surface, Kummers surface, number patterns, curves, topology, catenoid, numerical expressions, wallpaper patterns, graphics, galleries.
Subject: Applied Mathematics>Mathematics for Humanities>Decorative Arts and Design,
Geometry and Topology,
Geometry and Topology>Plane Geometry>Patterns>Geometric Patterns,
Geometry and Topology>Plane Geometry>Patterns (Plane Geometry)

Mathematical patterns in African American hairstyles
by Gloria Gilmer (1998)
[http://www.math.buffalo.edu/mad/special/gilmer-gloria_HAIRSTYLES.html]
This article discusses mathematical patterns used by hair braiders in African American communities. Even though the hair braiders don't think of themselves as mathematicians, they use geometric relationships in many of their designs. Using rotation, reflection, and translation of the original shape, tessellations are formed. These tessellations are most commonly found in box and triangular braids. Four classroom activities are provided. Other terms: culture, hair weaving, hexagon, square, triangle. (Includes 10 references)
Subject: Applied Mathematics>Mathematics for Humanities>Decorative Arts and Design>Hairstyles,
Cultural Context>Influence of Culture on Teaching Mathematics>Multicultural Approaches to Teaching,
Geometry and Topology>Plane Geometry>Patterns (Plane Geometry)
Geographical area: United States of America
Cultural group: African American

Mathematics and crafts in Andalusia: an anthropological-didactic study
by Mar�a Luisa Oliveras Contreras (1997)
[http://www.ethnomath.org/resources/ISGEm/097.htm]
This article describes the methodology for an anthropological study of mathematics use to produce typical crafts of Andalusia, Spain. The aim is to discover the degree of the social use of intuitive geometry in craft production and the relationship between school and popular mathematics. Marquetry, musical instruments, landscaping, Granada pottery, dressmaking, sculpting, carving, carpet weaving, stained glass, crochet, lace making, bronze and glass, iron and copper forging, Alpujarra textiles, goldsmithing, jewelry making, embroidery, and graphic arts were studied in relation to their use of shapes, angles, symmetry, translations, tessellations, Thales’ Theorem, Pythagorean Theorem, and symbolization. Greatest use was in stonelaying and dressmaking. Most craftsmen were not aware that their use of geometry, calculations, and measurements related to mathematics. Other terms: cultural heritage, abstraction, teacher preparation. (Includes 1 reference)
Subject: Applied Mathematics>Engineering Mathematics>Design and Construction of Household Items,
Applied Mathematics>Mathematics for Humanities>Decorative Arts and Design,
Cultural Context>Cultural Diversity>Popular Mathematical Practices (Street Math),
Geometry and Topology>Plane Geometry>Measurement (Plane Geometry),
Geometry and Topology>Plane Geometry>Patterns (Plane Geometry)
Geographical area: Andalusia (Spain), Spain
Cultural group: Andalusian

Origami & math
by Eric Andersen (1999)
[http://www.paperfolding.com/math/]
This website explores the connection between origami, the art of folding paper, and math. The study describes how origami can clearly be connected with geometry. It covers Kawasaki’s Theorem (i.e., “if you add up the angle measurements of every other angle around a point, the sum will be 180.”). The report also mentions the “straight edge and compass” construction (which can be encompassed by four basic axioms, as Euclid defined over 2000 years ago). Also included are Huzita’s Axioms, in addition to an origami theorem that can be viewed as either topological or combinatorial. The website provides links to diagrams (e.g., on how to create a paper dinosaur or a hummingbird), as well as to classroom ideas and origami history. (Includes a list of other resources on origami and mathematics)
Subject: Applied Mathematics>Mathematics for Humanities>Decorative Arts and Design,
Applied Mathematics>Mathematics for Social Sciences>Games and Toys,
Cultural Context>Cultural Diversity,
Geometry and Topology>Plane Geometry>Patterns>Geometric Patterns,
Geometry and Topology>Plane Geometry>Patterns>Symmetry,
Geometry and Topology>Plane Geometry>Fractal Geometry,
Geometry and Topology>Plane Geometry>Patterns (Plane Geometry),
Geometry and Topology>Plane Geometry>Transformations,
Numbers and Computation>Patterns and Sequences>Geometric Sequence,
Numbers and Computation>Patterns and Sequences (Arithmetic)

Recent ethnomathematical research in Mozambique
by Paulus Gerdes (1991)
[http://www.ethnomath.org/resources/ISGEm/054.htm]
This article summarizes a project in Mozambique that attempts to uncover the hidden mathematics in the daily life of the Mozambican people. The researchers use anthropological methods, developed in prior projects, to uncover and reconstruct the hidden mathematics used in the geometrical forms of objects such as baskets, mats, and pots. Other terms: Pythagorean theorem, monolinear patterns, Egyptian tombs, houses, fishtraps, symmetry, cultural values, ideograms, sona, sand drawing, pictogram, monolinear, mnemonic. (Includes 7 references)
Subject: Applied Mathematics>Mathematics for Humanities>Decorative Arts and Design>Sona,
Cultural Context>Cultural Perspectives on Mathematics,
Geometry and Topology>Plane Geometry>Patterns (Plane Geometry)
Geographical area: Angola, India, Mozambique, Zambia
Cultural group: Chokwe (Tchokwe) (Africa), Luchazi (Zambia), Makonde (Mozambique), Mozambican, Tamil (South India)

The Ethnomathematics Digital Library is a component of the National Science, Technology, Engineering and Mathematics Education Digital Library (NSDL), funded by the National Science Foundation.