Friday, October 3, 2014

Math update: Struggling through a dry spell

I was working on  the third installment of my Squaring the Circle series, in which I’d intended to relate what I’d learned about the nature of pi – I said I was pretty excited about it, and I really was!  I only wish I’d written that section this spring when I was still glowing from that Eureka! moment.  It’s a lot harder to write about all these weeks later, so instead* I’m reading the whole chapter on the Ancient Greeks in A History of Mathematics – before I just read the sections dealing specifically with measuring a circle.

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But here’s something fascinating about this chapter – I met nearly all of these people when I read John Mark Reynolds’ When Athens Met Jerusalem this spring and summer.  Did you know that Thales, the first philosopher, was also the first mathematician?  I didn’t, which is why I was so surprised when I wrote this post on Math and Philosophy.

All the early mathematicians were philosophers.  In fact, it is said that Pythagoras is the one who coined the words philosophy, “love of wisdom,” and mathematics, “that which is learned.” 

“Perhaps the most striking characteristic of the Pythagorean order was the confidence it maintained in the pursuit of philosophical and mathematical studies as a moral basis for the conduct of life.” (Merzbach and Boyer, p. 44)

More interesting passages from this chapter:

“ . . . mathematics was more closely related to a love of wisdom than to the exigencies of practical life.”

“Greek mathematics, in its earlier stages, frequently came closer to the ‘modern’ mathematics of today than to the ordinary arithmetic of a generation ago.”

“[T]he Pythagoreans not only established arithmetic as a branch of philosophy; they seem to have made it the basis of a unification of all aspects of the world around them.”

“The point of view of the Pythagoreans seems to have been so overwhelmingly philosophical and abstract that technical details in computation were related to a separate discipline, called logistic. This dealt with the number of things, rather than with the essence and properties of number as such, matter of concern in arithmetic. That is, the ancient Greeks made a clear distinction between mere calculation, on the one hand, and what today is known as the theory of numbers, on the other. . . .  [T]he early Ionian and Pythagorean mathematicians [have] the primary role in establishing mathematics as a rational and liberal discipline.”

That’s from the first half of the chapter.  There are sections coming up headed “Mathematics and the Liberal Arts,” and “The Academy,” so I’m looking forward to what else the authors have to say about that.

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I had a brief moment of elation today when one of my friends shared a math quiz on Facebook. 



There was one moment of panic involving multiplying a four-digit number by a two-digit one – the rest I was able to do in my head, but I had to pull out pen and paper for this one.  Oh, and there was one other that threw me, but my violin daughter was watching over my shoulder at that moment and said, “Think of it this way . . .” and then I was able to do it in my head.

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Here’s an interesting article you should read – Research on the Teaching of Math, which I think is a reprint of the appendix of the same name in Harvey and Laurie Bluedorn’s book Teaching the Trivium. They cover what they’ve learned of the history of teaching math, research on brain development, and suggestions for what to do with your own children.

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* Here’s a bonus article:  Why Writers Are the Worst Procrastinators.  I printed it out two days ago, but I’ve been avoiding reading it because I’m afraid it’ll be depressing.
:-p



2 comments :

  1. We're reading *Mathematicians are People Too* during circle time and have read about Thles and Pythagoras so far. We are enjoying it, and I knew about Thales :)

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    1. That looks like an interesting book -- thanks for the heads up! My lousy library only has one mathematician book, but it's about Paul Erdos and we read it, so I knew who he was when somebody or other mentioned him in a blog post last week.

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