Monday, September 8, 2008
Homework due 9/10/08
Read the excerpt on Euclid from the book A History of Mathematics: An Introduction, by Victor J. Katz and take good notes on the reading. Then comment on this post and pose questions that you have on the reading. You may also answer each others' questions using the blog. What I am hoping for is some meaningful dialogue about the reading before our block period class on Wednesday.
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10 comments:
I must admit,I was suprised by the length of the article you gave us, but I think my notes are sufficient. Most of the axioms I knew, just not in that wording. I'm also surprised that no one else has posted a comment...Hmm...oh well.
Maybe they are studying for the quiz tomorrow...But I'm glad you understood the reading!
I understand the postulates and "common notions", but what is the differance between an axiom and a theorem? Also, what is the differance between a number and magnitude? I have an idea, but not a clear picture.
I had the same question as Victoria. I find it wild that a book like this was so wildly accepted, maybe seeing as now-a-days we like instant gratification. Can somebody help me to understand the definition/postulate of parallel lines?
Steven, If one line crosses two lines that are not perfectly straight, four angles are formed in the inside of the two lines. If you add up the two angles for either side, one will be greater than 90, and the other less. Eventually the two lines will meet/intersect on the side where the two angles are less than 90 degrees. Hope this helps.
I think I understand the postulates and the "common notions", but I don't understand the difference between number and magnitude either. Can anyone explain it?
The common notions and postulates I can picture pretty well. Axioms, theorems, and the difference between number and magnitude are still puzzling, also can anyone think of a better definition for rectilinear? Victoria I think I understand your definition of the parallel postulate, thank you!
the article took me a while to read since there was a lot of information in it, but i think i understood most of it.
Well although I am pretty much the last to post...again, I still think the reading was helpful on understanding the axioms themselves while giving us a short history lesson. But it did seem to use unusual wording. (OH WAIT! Its Euclid...That would explain it.)
-broseph.
Some great and pressing questions so far folks. Do remind me to talk about number and magnitude in class tomorrow. As for Lauren's question about a better definition of rectilinear, it's all related to the distinction between a straight line and a line. Notice that Euclid considers the circumference of a circle as a line as well. When circles intersect, they too form angles at the points of intersection, but they are just not considered rectilinear.
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