/sci/ - Science & Math

How do i solve those:
1) R^3 can be decomposed into disjoint union of unit circles
2) R^3 can be decomposed into a disjoint union of straight lines, none of which are parallel
should be some kind of transfinite induction but i don't see it

>>12410456
well known fact - the rational points are dense in unit circle
then, you can join solutions in the following manner:
if x^2 + y^2 = 1 and a^2 + b^2 = 1, then (ax)^2 + (ay)^2 + b^2 = 1
and fuck around with induction and probably you'll get that rational points are dense in S^N

alternatively, use the standard method for finding rational points of degree 2 polynomial equation

>>11566881
god i beg you BEG YOU at least grace us with the pictures of her feet or anything really