Re: A little lesson for sqrt(144) year olds.
From: Eric Gisse (fsegg_at_uaf.edu)
Date: 07/07/04
- Next message: ZZBunker: "Re: Who are the richest men in world history?"
- Previous message: Eric Gisse: "Re: A little lesson for sqrt(144) year olds."
- In reply to: Androcles: "Re: A little lesson for sqrt(144) year olds."
- Messages sorted by: [ date ] [ thread ]
Date: 7 Jul 2004 02:07:12 -0700
"Androcles" <androc1es@nospamblueyonder.co.uk> wrote in message news:<x5jGc.331$rk4.5112897@news-text.cableinet.net>...
[snip]
> | Carefully taking square roots, one gets:
> |
> | x + b/(2a) = +/- sqrt(b^2 - 4ac) / (2a)
> |
> | and the formula follows.
>
> Goodness me! I'm told sqrt is always positive by Dinky the Deranged.
> Where did the minus sign in front of it come from?
Follow the math if you can, and find the error. Otherwise don't whine.
>
>
>
> |
> | An alternative, slightly more logical, derivation, might involve
> |
> | x^2 + bx/a + c/a = 0
> | x^2 + bx/a = -c/a
> |
> | and then asking the question "How do I complete the square here?".
> |
> | Algebra, IIRC, is taught in 8th-9th grade level, so this wouldn't be
> | that much of a stretch.
> |
> | >
> | >
> | >>
> | >> | Otherwise how would equalities such as sin(Pi/4) = sqrt(2)/2 make any
> sense
> | >> | at all? Surely you wouldn't claim that sin is dual-valued?
> | >> That rather depends on whether you use (x, iy) or (x,y), doesn't it?
> | >> Androcles.
> | >
> | > You know nothing of complex numbers.
> |
> | (x, iy)? Somebody's extremely confused. The usual representations
> | are (x,y) (or, if one prefers, (Re(z), Im(z))) or x + iy = Re(z) +
> i*Im(z).
> | Or perhaps Re(z) + Im(z); I don't remember offhand whether Im(z) returns
> | a multiple of sqrt(-1) or not. (I doubt it.)
> |
> | Of course completing the square works even for equations with
> | b^2 - 4ac < 0; the result is, of course, a complex number.
> |
> | x^2 + 1 = 0 in particular has a = 1, b = 0, c = 1; b^2 - 4ac = -4;
> | (-b + sqrt(b^2 - 4ac))/(2a) = +sqrt(-1) = i.
> | (The other root is of course -i.)
> |
> | >
> | >>
> | >> |
> | >> | / Jesper P
> | >> |
> | >> |
> |
> |
> | --
> | #191, ewill3@earthlink.net
> | It's still legal to go .sigless.
>
> Since we have mathematician in our midst, comments on
> http://www.androc1es.pwp.blueyonder.co.uk/Fundamental_rev_2.3.htm ?
> Androcles
Idiot. Just like Henri Wilson, and in the same way too.
- Next message: ZZBunker: "Re: Who are the richest men in world history?"
- Previous message: Eric Gisse: "Re: A little lesson for sqrt(144) year olds."
- In reply to: Androcles: "Re: A little lesson for sqrt(144) year olds."
- Messages sorted by: [ date ] [ thread ]
Relevant Pages
|
