Darrah Chavey: Ethnomathematics (Beloit College)

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source: Darrah Chavey     2016年8月28日
The ethnomathematics of a drawing tradition from Congo, Angola, and Zambia. Sona drawings, often done in the sand, are a one-line drawing form (i.e. an "Eulerian graph") used for decorations, but also used to transmit stories, lessons, and moral and cultural values to the boys in the months-long "coming of age" classes.

Ethnomathematics Lecture 2: Central Symmetry Groups (Revised) Beloit College, Math 103: On Central Symmetry Goups (Cn and Dn), the "products" of two symmetries, and Da Vinci's Theorem about Central Symmetry Goups. Cultural example on Southwest American Indians and 4-fold rotations. 1:11:57
Ethnomathematics: Sona Designs from Africa The ethnomathematics of a drawing tradition from Congo, Angola, and Zambia. Sona drawings, often done in the sand, are a one-line drawing form (i.e. an "Eulerian graph") used for decorations, but a...  48:16
Ethnomathematics: Number Words The meanings of the words used for numbers in different languages, and how larger numbers are constructed from smaller numbers in many different ways. 53:31
Ethnomathematics Lecture 13: Number symbols Beloit College, Math 103: The symbols various cultures have used to write, or transcribe, numbers. 31:10
Ethnomathematics Lecture 12: Win Trees for Games. Achi, Mancala Beloit College, Math 103: Using game trees from specific positions, e.g. 1- or 2-ply trees, to analyze a position. Using longer game trees from a position to demonstrate it's a winning position. Ex... 58:03
Ethnomathematics Lecture 11: Game Charts & Blockade Games Beloit College, Math 103: Using Game Charts to analyze maximal blockade games. Using lookahead to simplify such analysis. Examples include Pong Hau K'i (from China) and equivalent games from Korea,...53:59
Ethnomathematics Lecture 10: Game Trees and Game Charts Beloit College, Math 103: Creating Game Trees and Game Charts to analyze puzzles and games, and using lookahead to simplify such trees and charts. Examples include "River Crossing" problems (9th ce... 57:46
Ethnomathematics Lecture 9: Introduction to Puzzles and Games Beloit College, Math 103: Logic puzzles, or Combinatorial puzzles, and their analysis. The use of Game Trees to solve such puzzles. Examples include "Three Mug" problems (15th century Europe), and ... 59:05
Ethnomathematics Lecture 8: Double Strips & Compound Patterns Beloit College, Math 103: Designs created by combining copies (Double Strips) or interlacing pairs of patterns (Compound Patterns). Understanding orbits of motifs in a design. 40:59
Ethnomathematics Lecture 7: Symmetry Breaking Beloit College, Math 103: When a culture uses some technique to deliberately break the symmetry of a design, and when they do so on a geometrically regular basis, we would like to be able to model ... 1:03:29
Ethnomathematics Lecture 6: Symmetry Combinations Beloit College, Math 103: Using the calculations of combinations of symmetries to classify the possible perfect 2-colorings in strip patterns. Applying the same ideas to designs with two "similar",... 1:01:54
Ethnomathematics Lecture 5: Color Symmetries Beloit College, Math 103: Color symmetry patterns. 54:12
Ethnomathematics Lecture 4: Wallpaper Symmetry Beloit College, Math 103: Wallpaper (all-over) symmetry groups, and classifying the 17 types of symmetry groups. Cultural Example: Symmetry preferences of Hmong sub-groups. 1:03:49
Ethnomathematics Lecture 3: Strip Symmetries Beloit College, Math 103: On the 7 strip symmetry groups, with the beginnings of why the "other 5" cannot exist. Cultural Examples: Tibetan Sand Mandalas vs. Norwegian Rosemaling. 59:00
Ethnomathematics Lecture 2: Central Symmetry Groups Beloit College, Math 103: On Central Symmetry Goups (Cn and Dn), the "products" of two symmetries, and Da Vinci's Theorem about these groups. Cultural example on Southwest American Indians and 4-fo... 47:52
Ethnomathematics Lecture 1: Geometric Designs & Symmetries Beloit College, Math 103: On geometric designs and the four basic symmetry types: Rotations, Reflections, Translations, and Glide-Reflections. Cultural Example: Egyptian art has no glide-reflections. 47"51