Drexel dragonThe Math ForumDonate to the Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » Education » math-teach

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Peter Duveen

Posts: 163
From: New York
Registered: 4/11/12
Re: Square root of six
Posted: Aug 30, 2012 7:42 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Kirby, there is a nice method to calculate the log of a number using continued fractions.

Say, you have 4 = 10^x. This method allows you to evolve a numerical value for x by solving that equation using continued fractions. It's a bit tedious, but interesting. Curious and thoughtful students will always wonder how they can actually calculate the log of a number from first principles. A teacher should be able to supply an answer.

This method is in a mid-nineteenth century mathematics text I came across in Google Books.

Another method that was not taught in my student days is polynomial division. Newton was familiar with the method, and uses it to expand an expression into an infinite series. I used it recently to derive a formula for the difference between two variables, each raised to the nth power, where n is an integer. The answer is something like a^n - b^n = (a - b)[a^(n-1)b + a^(n-2)b^2....+ ab^(n-2) + b^(n-1)].

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2016. All Rights Reserved.