Motivated by mathematical aspects of origami, Erik Demaine asked which points in the plane can be constructed by using lines whose angles are multiples of $\pi /n$ for some fixed $n$. This has been answered for some specific small values of $n$ including $n=3,4,5,6,8,10,12,24$. We answer this question for arbitrary $n$. The set of points is a subring of the complex plane $\mathbf {C}$, lying inside the cyclotomic field of $n$th roots of unity; the precise description of the ring depends on whether $n$is prime or composite. The techniques apply in more general situations, for example, infinite sets of angles, or more general constructions of subsets of the plane.

The optimal management of moderate-to-severe hypothermia with hemodynamic instability remains unclear. Although cardiopulmonary bypass offers the most rapid rate of rewarming and has been suggested as the method of choice in the presence of circulatory arrest, there is no evidence to support the use of this highly invasive technique over other rewarming modalities in the absence of circulatory collapse. We report the successful treatment of hemodynamically unstable hypothermia with conventional hemodialysis in a patient with normal renal function, after initial efforts of rewarming using conventional strategies had failed. This case report and review of the literature highlights the advantages and the challenges of using hemodialysis in this setting, and suggests a potential role for hemodialysis in the routine management of moderate-to-severe hypothermia in the absence of circulatory arrest.