# Ethnomathematics: Mathematics and Culture

## Video Lectures

Displaying all 13 video lectures.
 Lecture 1 Play Video Geometric Designs & SymmetriesGeometric designs and the four basic symmetry types: Rotations, Reflections, Translations, and Glide-Reflections. Cultural Example: Egyptian art has no glide-reflections. Lecture 2 Play Video Central Symmetry GroupsCentral 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-fold rotations. Lecture 3 Play Video Strip Symmetries7-strip symmetry groups, with the beginnings of why the "other 5" cannot exist. Cultural Examples: Tibetan Sand Mandalas vs. Norwegian Rosemaling. Lecture 4 Play Video Wallpaper SymmetryWallpaper (all-over) symmetry groups, and classifying the 17 types of symmetry groups. Cultural Example: Symmetry preferences of Hmong sub-groups. Lecture 5 Play Video Color SymmetriesThis lecture will cover color symmetry patterns. Lecture 6 Play Video Symmetry CombinationsUsing 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", but not identical, motifs. Cultural example: U.S. Depression glass. Lecture 7 Play Video Symmetry BreakingWhen 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 what it is that they are doing. Lecture 8 Play Video Double Strips & Compound PatternsDesigns created by combining copies (Double Strips) or interlacing pairs of patterns (Compound Patterns). Understanding orbits of motifs in a design. Lecture 9 Play Video Introduction to Puzzles and GamesLogic 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 Tchuka Ruma (Indonesia/Malaysia), a solitaire form of Mancala. Lecture 10 Play Video Game Trees and Game ChartsCreating 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 century Europe), Tic-Tac-Toe, and "Blockade" games from many countries. Pong Hau K'i as a Maximal Blockade game. Lecture 11 Play Video Game Charts & Blockade GamesUsing 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, India, and Thailand; Berry Patch Scramble from General Mills, and Mu Torere from the Maori (New Zealand). Introducing Achi, from Ghana. Lecture 12 Play Video Win Trees for Games. Achi, MancalaUsing 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. Examples with Achi (from Ghana) and a version of Mancala also from Ghana. Lecture 13 Play Video Number SymbolsThe symbols various cultures have used to write, or transcribe, numbers.