Assignments for Week 3/4
R = Readings ._._. W = Writings
- (R) In our online textbook read the Early Period part
of the chapter on Greece,
and the relevant part of "Background readings from the Internet"
(especially "Trisectrix animation", and also the "How do we know
..." pages).
Also read my "lecture" for the week
(when available).
- (RW) STANDING ASSIGNMENT EVERY WEEK:
Read the parts (if any) of your "general history" book
corresponding to this week's material.
You are encouraged to mail in ("report to the class") anything interesting or
important that you found in your reading that's not in the online material.
- (W) (For Friday, Sept. 26) From the
exercises on Early Greek mathematics:
- 2 (trisectrix formula)
- 3 (parity in Pythagorean triples)
- 5 (irrationality of roots)
- 12 (square root of 3)
- Your choice of any two of the remaining 11 problems.
(Submit geometrical constructions by paper mail if necessary.)
- (W) Two essay questions (also due 9/26):
- Explain Iaglom's dictum (quoted by both Allen and
Panchenko),
"In practical mathematics there can exist no irrational numbers."
Could one reasonably argue the contrary position?
- Although often regarded as the beginnings of science as we
know it,
the pronouncements of the early Greek thinkers sometimes strike
us as weird or meaningless.
Pick one figure from this period (not Thales, since
Panchenko has already covered him thoroughly) and discuss in a
paragraph or two (1) in what respects (if any) his ideas
(mathematics, science, philosophy) represent a qualitative
advance over what the Egyptian and Babylonian cultures apparently
had to offer; (2) what aspects of his work would be rejected
today as unscientific.
(In the second part, concentrate on basic methodological or
conceptual issues, not factual errors (like the size of the
sun) that have been superseded by modern data.)