From: bdsm@fermat.WPI.EDU (Billy Don McConnell)
Newsgroups: k12.ed.math
Subject: Re: help - need formula
Date: 9 Oct 92 00:25:42 GMT
Organization: Worcester Polytechnic Institute
NNTP-Posting-Host: fermat.wpi.edu
Originator: bdsm@fermat.WPI.EDU


In article <1b2f91INNofs@usenet.INS.CWRU.Edu>, cb919@cleveland.Freenet.Edu (Mike Bolduan) writes:
|> 
|> If you want a way to get "an answer" to a SPECIFIC cubic which is
|> accurate to a great many decimal places, then use a graphing
|> calculator or computer grapher to graph the appropriate equation
|> and zoom in on the x-interecepts until you have enough
|> accuracy.
|> On the other hand if you want a GENERAL formula to solve ALL cubics
|> (i.e., one in terms of A, B, C and D, then I would point you
|> toward some historical research -- you will want to look up
|> Giralmo Cardano (16th century) and his cubic formula. It is not
|> a pretty sight and certainly is never used ijn any practical sense.
|> It is moistly interesting for the story that goes with it -- which
|> I will let you find for yourself. Then you can move on to the
|> formula for the general FOURTH degree equation.....
|> (and I am cerytainly glad you did not ask for a formula for a
|> FIFTH degree equation....)
|> Perhaps you should have specified exactly what you had in mind
|> when you asked for a "solution" formula. 
|> I believe you can find both the cubic and the quartic foirmulas
|> in Heinrich Teitze's book Famous Problems of Mathematics.
|> (Oops, that shouold be Tietze)
|> 
|> mike bolduan
|> bolduan@catlin    on bitnet
|> bolduan@catseq.catl;in.edu   on internet
|> 
|> p.s. -- this wouldn't have been for a homework assignment would it??? :-)
|> -- 
|> mike bolduan
|> bolduan@catlin

You can also find it in these formulas (and they aren't as bad as all that,
when broken into small steps) in the CRC (that's Chemical Rubber Company...go
figure) _Standard Mathematical Tables_ book, at least one edition of which 
(that's all you'd need) should be within easy reach of anyone claiming to be
a serious mathematician.  The CRC is the Mathematician's Bible, at least it
is to me.  (I've had one since high school, and I've yellowed most of the
pages with my near-continual flipping.)

Some sections of the _Math Tables_ are reproduced as sections of other _Tables_
books, like the CRC _Physics Tables_ or _Chemistry Tables_.  These books should
be available in any well-rounded bookstore's "Reference" or "Math/Science" 
sections...especially in a college town.  I heartily recommend the purchase of
one.

Do I sound like I work for the CRC folks?  Sorry.  I should probably point out
that the majority of the CRC material is completely foreign and/or useless to me
(they include a lot of tables that are made obsolete in this age of pocket
computers); I only use (but use often) a fairly small portion of the book.
However, paging through the book on lazy afternoons has quite frequently opened 
my eyes to new things. Which is why I am going through all this:  sometimes a 
serious interest in Mathematics can be sparked by a simple glance through a rich 
resource of good ol' Math "stuff", without all the surrounding text.

So what starts out as a quest for the solution to a cubic equation might just
turn into a lifelong association with the beauty and wonder of Mathematics.
(Do I hear the national anthem?)

Billy Don Sterling Mc Connell
   (just call me "Don")

--Be fruitful and Multiply.
--Divide and conquer.
--There's strength in Numbers.