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Topic: Square root of six
Replies: 21   Last Post: Aug 31, 2012 12:47 PM

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Peter Duveen

Posts: 163
From: New York
Registered: 4/11/12
Re: Square root of six
Posted: Aug 30, 2012 10:03 AM
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Jonathan, thanks for the feedback. I downloaded the work of the Indian mathematician, and am looking forward to scanning through it.

I have just recommended the English translation of Euler's work on Algebra to some of my students. Now I shall bring this Indian work to their attention.

There's a lot to be gained by examining these older works. Many methods that have been long since thrown overboard may be gleaned from them. The historical progression of mathematics has always been of interest to me, as I am constantly asking the question, "Where did that come from," or "how was it that someone figured that out?" A simple example is the Taylor expansion. When I first heard of it, I was amazed that functions could be expanded as an infinite power series. It seemed to come out of the blue. When I finally found time to explore its origins, I came to understand that expansion of functions in power series predated the calculus. That, of course, makes much more sense. In teaching series, I think it is helpful, not to start with definitions, but to show that a function can be expanded as an infinite series. For example, the expression 1/1-x can be expanded as an "infinite" power series using polynomial division. This was known to Taylor before he developed his pow!
er series based on the derivatives of a function. So my point, I guess, is that, for the purposes of teaching, there is much to be gained from a knowledge of the historical sequence of mathematical development.



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