Topic 1: Quipu
- General Introduction
- Peruvian Civilization and the Inca Empire. Quick discussion on the Geo-Historical need for a record system.
- Introduction of the chasquis and the Quipukeeper as examples of historical adaptation to the orographic conditions.
- Quipu as written records? Brief analysis of Quipu as possible writing system as suggested by Professor Gary Urton in his analysis of the Historia Piruanorum.
- Structure of Quipu
- General Characteristics and string hierarchy: S and Z Strings. Introductory vs coding segments.
- Types of Knots: Single, Long and E-Knots
- Coding elements: Color of the strings and spacing on the strings.
- Arithmetical Ideas
- Positional base 10 numeral System. Supporting evidences for a possible base 5 system
- Addition with Quipu. Puruchuco quipu are an example of a progressive addition of hierarchical values These Quipu were likely used for bookkeeping and they are an example of summation of values -
- Ratios and Fractions Quipu used in population grouping and tax regulations show a fundamental grasp of set theory and elemental partitions.
- Multiplication with Quipu Quick explanation of possible uses of quipu as calculators in complex multiplications. I will introduce the example of quipu 719 which is one of the few surviving Inca multiplication “tables” .
Topic 2: Plimpton 322.
- What is Plimpton 322?
- Origin of its name
- Reminder of how to read the Babylonian number system
- What do the numbers translate to?
- How is is relevant to now?
- Recent research about Plimpton 322
- What does this mean for math?
- Why is it significant in history?
- Pythagorean’s Theorem debate Is this the oldest trigonometric table?
- How may have the Babylonians calculated these numbers?