Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 2013-07-22 16:53:07

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,535

Euler's Formula for Complex Numbers

Had a go at explaining Euler's Formula for Complex Numbers

What do you all think?


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Offline

#2 2013-07-22 19:07:57

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,380

Re: Euler's Formula for Complex Numbers

hi MathsIsFun,

Another great page!  Well done!

I wish I could turn the clock back and get the inventor of 'imaginary numbers' to call them something else.  It has led to the unfortunate idea, held by some, that imaginary numbers have less validity than 'reals', because they are made up and don't really exist (whatever that means).

I believe that the proper reason for this name is that the second axis on the Argand diagram is the image of the first. Possibly you could add a note to this effect?

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

Offline

#3 2013-07-22 19:39:37

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,364

Re: Euler's Formula for Complex Numbers

Hi MIF;

Thanks for the page.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#4 2013-07-22 19:50:03

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,535

Re: Euler's Formula for Complex Numbers

bob bundy wrote:

I believe that the proper reason for this name is that the second axis on the Argand diagram is the image of the first.

That would be a nice reason, but I believe "imaginary" was used to ridicule them, until they found the complex realm was a hidden truth behind many things.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Offline

#5 2013-07-22 19:55:21

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,364

Re: Euler's Formula for Complex Numbers

Hi;

Some books give the credit to Descartes who was ridiculing them.

In 50 A.D., Heron of Alexandria studied the volume of an impossible section of a pyramid.  What made it impossible was when he had to take √(81-114).  However, he deemed this impossible, and soon gave up.

Issac Newton agreed with Descartes, and Albert Girad even went as far as to call these, “solutions impossible”

Interesting!


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

Board footer

Powered by FluxBB