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Video Lectures

Course

Code:	MATH 103
Subject:	Mathematics
Views:	17,051

Educator

Name:	Beloit College (Beloit)
Type:	University

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Ethnomathematics: Mathematics and Culture

Video Lectures

Displaying all 13 video lectures.

Lecture 1 Play Video	Geometric Designs & Symmetries Geometric 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 Groups 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-fold rotations.
Lecture 3 Play Video	Strip Symmetries 7-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 Symmetry Wallpaper (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 Symmetries This lecture will cover color symmetry patterns.
Lecture 6 Play Video	Symmetry Combinations 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", but not identical, motifs. Cultural example: U.S. Depression glass.
Lecture 7 Play Video	Symmetry Breaking 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 what it is that they are doing.
Lecture 8 Play Video	Double Strips & Compound Patterns Designs 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 Games 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 Tchuka Ruma (Indonesia/Malaysia), a solitaire form of Mancala.
Lecture 10 Play Video	Game Trees and Game Charts 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 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 Games 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, 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, Mancala 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. Examples with Achi (from Ghana) and a version of Mancala also from Ghana.
Lecture 13 Play Video	Number Symbols The symbols various cultures have used to write, or transcribe, numbers.