This is a 2 talk series (part 1, part 2: this part).
We will show that there is a model of \({\rm ZF}\) with no well order on the reals in which there is a partition of \(\mathbb{R}^3\) in unit circles. The major obstacle is satisfying some amalgamation, for which geometrical and algebraic considerations are needed. If the time allows, we will see how these techniques can generalize to other applications.