SOLVING FOR THE ROOTS OF

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2 total messages Started by Sheila King Sun, 10 Jan 1993 19:44

#484

Author: Sheila King
Date: Sun, 10 Jan 1993 19:44

29 lines
1695 bytes

To: Henry Choy

-> Are there any high school math classes where cubic root finding,
-> fundamental theorem of arithmetic, Newton's method, etc. are taught?

In my Honors Pre-Calculus class, we do not teach how to find exact cubic
roots by the method for cubic equations similar to the quadratic
formula. However, we did show how to find estimates of irrational roots
of a cubic to any desired degree of accuracy by what our text calls "The
Midpoint Algorithm". This algorithm is very similar in approach to
Newton's Method, but doesn't require calculus.

Newton's Method would (I imagine) be only taught in calculus classes.

Could you tell me what the fundamental theorem of arithmetic is? I know
the fundamental theorems of algebra and calculus, but I didn't know
there was one for arithmetic.

Sheila King

P.S.--as moderator I have two small requests: 1) could you please use
your real name in the TO: field instead of "I am a terminator". 2) would
you consider how effective it is to repeatedly post the "log song" from
Ren and Stimpy in your sign off?
                                                                                              

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Internet: Sheila.King@f315.n103.z1.fidonet.org

Fund. Thm. of Arithmetic

#487

Author: Bob Murphy
Date: Wed, 13 Jan 1993 02:39

29 lines
1427 bytes

In article <37005.2B527C15@puddle.fidonet.org> Sheila.King@f315.n103.z1.fidonet.org (Sheila King) writes:
>
>Could you tell me what the fundamental theorem of arithmetic is? I know
>the fundamental theorems of algebra and calculus, but I didn't know
>there was one for arithmetic.
>
>Sheila King
>

---------------------------------------------------------------
Fundamental Theorem of Arithmetic:

  Every positive integer n > 1 can be expressed as a product 
  of primes; this representation is unique, apart from the 
  order in which the factors occur.
---------------------------------------------------------------

This unique factorization is an important property of positive
integers and is the reason that 1 should never be considered
a prime number.  If 1 were considered a prime number then we 
would have, for example:

       6 = 2*3
       6 = 1*2*3
       6 = 1*1*2*3
       etc.


                   Bob Murphy (rmurphy@aludra.usc.edu)

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