Isn't it possible to just take the union of all helices of the form: H_(x,y) := {(cos(t) + x, sin(t) + y, t) | t in R}
Sent: Saturday, September 26, 2015 at 7:56 PM From: "Dan Asimov" <asimov@msri.org> To: "Eugene Salamin" <gene_salamin@yahoo.com>, math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] Helix puzzle
Good point. I mean isometric via any isometry of R^3 (which includes translations and rotations).
—Dan
On Sep 26, 2015, at 11:51 AM, Eugene Salamin via math-fun <math-fun@mailman.xmission.com> wrote:
Do you mean translates and rotations of H ? Otherwise, a line is isometric to H.
From Dan Asimov on Saturday, September 26, 2015 11:13 AM:
Let H denote the standard helix in R^3, namely the set:
H := { (cos(t), sin(t), t) | t in R}.
Puzzle: -------
Express R^3 as the disjoint union of subsets each isometric to H, or prove this is impossible.
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