/sci/ - Science & Math

[Anonymous No.14554269]

is this guy just a loony case or is his stuff of any worth?
http://kinkytshirts.nl/rootdirectory/just_some_math/3d_complex_stuff.htm
http://3dcomplexnumbers.net/page/22/

[Anonymous No.14554275]

> j^3 = -1

j = -1

[Anonymous No.14554286]

I'm not gonna read all that shit, but yes you can salvage a lot of things for objects that generalize the complex numbers with looser algebraic matrix relations

For example, already when

[math] J^2 J = j^2 J [/math]

where J is some operator and j is in a nice field, then the Euler formula in

[math] \exp(z\,J) = E + \dfrac{\sinh(z\,j)}{j} J + \dfrac{\cosh(z\,j)-1}{j^2} J^2 [/math]

where the special function here denote their known series expansions.
(Complex numbers are a special case of that where J^2=-1 and J=j)

That shouldn't come as a surprise:
If you got a polynomial Q of order n+1 and another P of order n and a relation
Q(J)=P(J),
then any infinite order series (say exp) formally will have a representation that only involves terms of order n. This is because you can use your algebraic relation to turn all J^(n+1) to an (potentially nasty) polynomial of max order J^n.
X^2 = -1
is an extreme example.

[Anonymous No.14554292]

>>14554286
ah, good to know, thanks

[Anonymous No.14554297]

[math] \displaystyle
\boxed{ \mathbb{T} \;
\boxed{ \mathbb{S} \;
\boxed{ \mathbb{O} \;
\boxed{ \mathbb{H} \;
\boxed{ \mathbb{C} \;
\boxed{ \mathbb{R} \;
\boxed{ \mathbb{Q} \;
\boxed{ \mathbb{Z} \;
\boxed{ \mathbb{N}}}}}}}}}}
[/math]

[Anonymous No.14554332]

>>14554297
what do you make of these pics of his?
i have barely read his stuff, but from what little i have gazed i already know that he is quite the character

[Anonymous No.14554335]

>>14554332

[Anonymous No.14554337]

>>14554335

[Anonymous No.14554397]

>>14554269
I found that guy a while back.
He is loony, but the algebra looks sound. You don't even have to appeal to matrices to justify your algebra, although it is standard to do so.
What's loony is everything else.

[Anonymous No.14554890]

>>14554275
kek, everyone else in this thread is retarded

[Anonymous No.14555124]

>>14554890
A rotation by pi/3 has this property too

[Anonymous No.14555152]

>>14554275
If complex, there are three solutions. -1 being the naive solution.Dumb ass.