A polar sphere can be defined with
- angle x
- angle y
This results in a double cover etc. Buuuuut... the cool thing of course is in algebra, its (not)counting. But its algebra. thats cool enough anyway ;)
- IF r(a)+(b) <= this ismt wrong
- THEN you get two interpretations that inherently reduce by euler etc. see above. its an elegant circular argument, blabla etc.
- So, according to the universe, probably as to our limited understanding of that space, there is a reason for
1. zero, plus & minus & infinite geometries 2. because any complete path on unity sphere is global and without inversion no reduction. plots in 3d as a quaternion(path)