- Homework due next time: Sections 2.3 and 2.4
- Issues from sections 2.5/2.6:
- square plus sides
- What decimals in sexagesimal are terminating that don't terminate in base 10?
- A map of the ancient world showing the complexity of Babylon from the perspective of the Jews (and, more recently, the Christians)
- Commercial (Nathan) -- who's next? Adam; Tom for next Monday.
- Lessons from section 3.1
- Plimpton 322 (1900-1600 BCE): a tablet containing "Pythagorean triples" (many years before Pythagoras, 6th century BCE)
- How were the triples found?
- Sexagesimal system dictated the choice of the values of m and n
- Many tablets excavated from Susa (including Hammurabi's Law)
- From the Cairo papyrus (circa 300 BCE):
- Egyptians were aware of several Pythagorean triples.
- Examples of the ol' ladder problems (p. 78):
A ladder of 10 cubits has its foot 6 cubits from a wall; to what height will it reach? (Babylonian version: "A beam of length ...." p. 78)
- Solving problems by the addition of a special form of
zero:
- Babylonians: "Square plus sides" method produces
- Into Greece.... (source)
- The Greeks:
- travellers/migrants (p. 86)
- colonizers (colonies were "conduits through which Greek culture flowed to the world of the "Barbarians"....) (p. 86)
- Mathematics came from the colonies, not from Mainland Greece (p. 86)
- The Greeks took the Phoenician alphabet, and swapped some consonents for vowels. The Ionian variant was adopted "universally" in 403 BCE. (p. 86)
- Greeks of Asia Minor introduced coinage in 700 BCE.
- Their education helped create "gentleman amateurs" (rather than arcane priesthoods): education was for the masses. So was their language.
- "uninhibited": they had "no sacred writings or rigid dogmas that required the mind's subservience." (p. 87)
- Greeks cities worked as individuals. The city-states fought together, but could not easily be unified under a single ruler.
- Philip II of Macedonia finally unified Greece by defeating its combined forces at Chaeronea in 338BCE.
- Then Philip's son Alexander the Great (356-323 BCE) finished the job, and carried Greek civilization to the ends of the known world.
- The time from "...Alexander the Great into the first century B.C. ... formed a brilliant period of history known ... as the Hellenistic Age." (p. 88)
- Greek mathematics reached its zenith with Euclid, Archimedes, and Appolonius.
- Who was Thales of Miletus?
- Circa 625-547 B.C.
- First of the Seven Sages of Greece
- Credited with the maxim "Know thyself."
- Strangest thing he had ever seen: "An aged tyrant."
- Aesop's Mule (originally told by Plutarch -- search for Thales)
- Olive oil, tripping and falling, yada yada....
- Credited with heightening deductive reasoning in mathematics.
- Mathematics:
- See page 89. Do page 89!
- May have travelled to Egypt (knew Egyptian mathematics, at any rate), and credited with calculating the height of the Great Pyramid of Cheops.
- Credited with the method for calculating the distance of a ship from shore. Let's see if we can use this method to calculate the distance of an object on campus!
