Today:
- Announcements
- (Most of your tests) are graded. Some of you still have the "history" portion in my hands. I'll return what I have graded.
- Today:
- Lessons from the midterm
- Commercial from Kim; Wednesday - Katie; then Nathan?
- A few more lessons from 4.5
- Things went pretty well on the midterm. A few comments:
- I'll share a few of my favorites next time.
- Problem 2: nearly everyone did great. The only "systematic" problem was that some used the wrong Chinese system....
- Problem 3: this was a killer, but only 4 attempted it (and perhaps regretted it!). There are 50 positive Pythagorean triples with
-- but if you consider the negative ones, too, that makes 100! (even more, however....)
- Problem 4: Debra had a nice solution to the general coefficients of the m-agonal numbers.
- Problem 5: Various solutions
- Problem 6: Oddly a fair number of folks struggled with this one. We want to solve for x, the length of the main side (from which we can deduce the other). But many couldn't figure out what to do, particularly on part c.
- Problem 7: Duplation and Mediation (for Kim!;) I didn't get a really great solution to the "how", although I got two close answers. How does it work?
- Problem 8: Regular numbers. How do we prove show the necessary and sufficient conditions?
- Problem 9: Finger numbers. There is a breakdown in the method -- it is not enough to show that the appropriate identity is correct. For which values does the method fall flat? And how can one fix the problem?
- Mathematical Elements, lessons and problems from section 4.5: Archimedes and Apollonius
- Archimedes of Syracuse
- There's too much!
- Born, lived and died in Syracuse. Father Phidias an astronomer.
- "greatest creative genius of the ancient world"
- Of the royal family of King Hieron II
- Visited Egypt, and presumably knew the mathematicians of the
Museum in Alexandria (e.g. Eratosthenes)
- Images of Archimedes:
- Mathematics we should try:
- Calculating Archimedes's grave marker:
- Archimedes's cubic:
-
- Approximating
- The Palimpsest
- The Quadrature of the Parabola
- The Sand Reckoner
- Apollonius of Perga: The Conics
- Pity Apollonius, who is pitted against Archimedes in this section!
- Called "The Great Geometer" for his treatment of the theory of conics.
- Conics are obtained by slicing a right circular cone in different
ways.
- He named our favorite conics: parabola, ellipse, hyperbola
Website maintained by Andy Long.
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