- Your homework problems (for chapter 1) are not graded yet - sorry!
I'm working through 1.2.
I'm grading only some of the homework: (1(b c), 2(d a), 3(c a), 4, 5(c a), 6(d a), 7(d b))
(chosen at random).
- Worksheet for section 2.6 (for next time). We'll try to get caught up by combining 2.5 and 2.6 Wednesday.
- More lessons from Section 2.3
- Finish determinant example (double false position)
- Other lessons you'd like to see (and maybe one I'd like to see!;)
- Commercial -- Katie
- Lessons from Section 2.4
- (There is no way that we will get to) Lessons from Section 2.5
- Problem #22 -- "completion"
- Problem #24 -- false position
- Fibonacci's egg problem -- false position (how many eggs?)
- Double false position:
- Robert Recorde, born 1510; author of Grounde of Artes:
- 'finding the true result from the chance answers of "such children or idiots that happened to be in the place."'
- Problem #28 -- "think of a number"
- Problem #79 -- sum of a geometric series?
- Some major ideas/issues:
- geometry = "earth" + "measure"
- Egyptians were seen as practical "rope stretchers". According to Kline (and our author, p. 78), there is no evidence that the rope stretchers of ancient times used the 3/4/5 rope to determine right angles, but they must have had pretty good alternative methods!
- Couldn't seem to get quadrilateral areas right:
-
- (Temple of Horus at Edfu (100 BC))
- What is an example of a quadrilateral that would be really poorly represented by this formula?
-
- As of the rhind papyrus had
- But the Babylonians of the tablet of Susa used 3;7,30 or
- Early Babylonians and Hebrews used
(see I Kings 7:23, circa 650 BCE)
- Pyramid
of Cheops (2600 BC)
- Largest building of ancient times
- Height: 481.2 feet; Width: 755.78 feet (
)
- "the base is almost a perfect square...." p. 59
- Oriented NWSE by less than 1 degree
- golden ratio (
) and
hypothesized "within"
- What do you think of the pyramidiots?
- "The geometry of the period lacked deductive structure...."
- Problem #50 -- formula for the area of a circle
- Don't know how
- Proposal: approximation of circles by octagons (Problem 48)
- "...this is nearly the value...." I don't think much of our author's "possible explanation" of the approximation formula of the Egyptians.
- What formula (and value of
- Don't know how
- Problem #52 -- Area of a trapazoid
- Problem #14 (of 25) of the Moscow papyrus (the "masterpiece of
ancient geometry")
- Do the Egyptians of 1850 BCE know the formula for the volume of a truncated square pyramid?
- This problem can be attacked using the approach of "similar pyramids".