Message #2731

From: Roice Nelson <>
Subject: Re: [MC4D] Re: Puzzle in Minkowski Space?
Date: Thu, 02 May 2013 22:46:20 -0500

On Thu, May 2, 2013 at 5:45 PM, schuma wrote:

> My question is more about, can we define 3D puzzles that fill a 3D region
> in a Minkowski 2+1 space?

Maybe a starting point to get to a "solid" object in the space would be to
change the expression for the surface of a constant radius to an
inequality, i.e. rather than:

x^2 + y^2 - t^2 = -1 (surface of hyperboloid of two sheets)

do this:

x^2 + y^2 - t^2 >= -1 (see 2D slice of
wolfram alpha. Also, it’s interesting that the "radius" is negative.)

Then you could slice up that solid with planes. So it seems like a good
thing to understand is what is a plane in M3 (2+1 Minkowski space). The
following article, "Hyperbolic Geometry on a Hyperboloid" looks to offer
lots of good information about M3:

M3 planes through the origin result in geodesics on the hyperboloid
surface. Planes not through the origin results in circles (or horocycles
or curves equidistant to geodesics) on the surface. This all seems to
suggest that the puzzle result might be functionally the same as MagicTile
puzzles though. Even if a solid object, the slicing of the stickers on the
boundary might end up the same with the approach I’m describing.

But maybe one could build up some solid objects in M3 with planes, rather
than starting with this "imaginary sphere" surface. And perhaps there
could be new effects from that, especially say, if the object boundary
moved into the area of the Minkowski space outside the "light cone". For
example, what would be the meaning of a dodecahedron plopped straight
inside M3?

I hope you can come up with some new and unique puzzle concepts and puzzles!