Services & ResourcesWolfram ForumsMathGroup Archive

[Date Index] [Thread Index] [Author Index]

Re: Re: Imaginary numbers - most interesting points

• To: mathgroup at smc.vnet.net
• Subject: [mg98750] Re: [mg98739] Re: [mg98647] Imaginary numbers - most interesting points
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Sat, 18 Apr 2009 03:36:09 -0400 (EDT)
• References: <200904150859.EAA07983@smc.vnet.net> <3508f1db0904160744r3017eea8x6796b974a2ffc67@mail.gmail.com> <200904170829.EAA23490@smc.vnet.net>

If you want something a little more ambitious ;-) you can get hold of  
the book "Abel's Theorem in Problems and Solutions. Based on Lectures  
of Professor V.I. Arnold" by V.B. Alekseev, published by Springer- 
Verlag in 2004. As the title says, it is based on lectures given by  
V.I. Arnold in 1963-64 (for half a year) to Moscow school-children.  
The lectures start with the usual formula for solving quadratic  
equations and finish with a new proof of Abel's theorem on the  
impossibility of solving in terms of radicals of equations of degree 5  
and higher. Chapter 2 is all about complex numbers. In the meantime  
they cover group theory, topology and in particular the theory of  
Riemann surfaces. I don't know how many of the children who listen to  
the original lectures understood it all, but at least one must have  
done since he. many years later. wrote this book.

Andrzej Kozlowski


On 17 Apr 2009, at 17:29, robert prince-wright wrote:

>
> thanks for the Gauss quote Peter
> its amazing to realise how bad maths teaching is. If you were taught  
> how multiplying by 'i' is effectively a 90 degree rotation and that  
> i squared added another 90 deg then Cauchy Riemann, stream and  
> potential functions all make more sense...
>
>
>
>
>
>
>
> ________________________________
> From: peter <plindsay.0 at gmail.com>
> To: robert prince-wright <robertprincewright at yahoo.com>
> Cc: mathgroup at smc.vnet.net
> Sent: Thursday, April 16, 2009 9:44:56 AM
> Subject: [mg98739] Re: [mg98647] Imaginary numbers - most  
> interesting points
>
> "That this subject [imaginary numbers] has hitherto been surrounded  
> by mysterious obscurity, is to be attributed largely to an ill  
> adapted notation. If, for example, +1, -1, and the square root of -1  
> had been called direct, inverse and lateral units, instead of  
> positive, negative and imaginary (or even impossible), such an  
> obscurity would have been out of the question. " -Gauss
>
> Peter
>
>
> 2009/4/15 robert prince-wright <robertprincewright at yahoo.com>
>
>
> I have (perhaps unwisely!) decided to do a 'Pecha Kucha' on  
> imagination .... or at least imaginary numbers. The audience are all  
> engineers with hazy recollection of undergrad maths.
>
> If you are not familiar with Pecha Kucha, then its worth checking  
> Youtube and doing some googling. Simplistically the concept is to  
> share understanding of something using 20 slides. Each slide should  
> convey as much as possible with as few words as possible, with the  
> message limited to 20 seconds!
>
> So, what is the most interesting thing about the imaginary number  
> 'i' that you can think of, and how can it most simply be conveyed  
> using Mathematica 7 in Slide presentation form?
>
> I've started with the notion of polynomial roots, de Moivre,  
> reflections etc. but would appreciate a wider view.
>
> R
>
>
>
>
>
>
>
> -- 
> Peter Lindsay
>
>
>
>
>

• References:
  • Imaginary numbers - most interesting points
    • From: robert prince-wright <robertprincewright@yahoo.com>
  • Re: Imaginary numbers - most interesting points
    • From: robert prince-wright <robertprincewright@yahoo.com>