Re: [math-fun] ridiculously simple derivation (whose?) of Pythagorean triples

26 Apr 2013


      The same thing also comes out from

   |z|  =  |conj(z)|  =>

    1^2 =  |K + iL|^2 / |K - iL|^2  =  |(K + iL) / (K - iL)|^2

        =  |(K + iL)^2 / (K^2 + L^2)|^2  

        =  |(K^2 - L^2) + i2KL|^2 / (K^2 + L^2)^2

--Dan 


On 2013-04-26, at 1:04 AM, Bill Gosper wrote:
...
In[570]:= (1+2*I)/(2+1*I)
Out[570]= 4/5+(3 I)/5
In[571]:= (1+3*I)/(3+1*I)
Out[571]= 3/5+(4 I)/5
In[572]:= (2+3*I)/(3+2*I)
Out[572]= 12/13+(5 I)/13
In[573]:= (1+4*I)/(4+1*I)
Out[573]= 8/17+(15 I)/17
In[586]:= Simplify/@ComplexExpand[(a+I*b)/(b+I*a)]
Out[586]= (2 a b)/(a^2+b^2)-(I (a^2-b^2))/(a^2+b^2)

Re: [math-fun] ridiculously simple derivation (whose?) of Pythagorean triples

Dan Asimov