Funny you should mention this; a few weeks ago I was reading in a post by Joel Hamkins about the 1-by-2-by-4 bricks that apparently are used in math education, and I read the claim that you can use two of these bricks to make a scaled up brick of the same kind, and I thought to myself “No, that would be a 1-by-2^(1/3)-by-2^(2/3) brick”. Jim Propp On Wednesday, June 20, 2018, Ed Pegg Jr <ed@mathpuzzle.com> wrote:
A cuboid with sides 2^(1/3) to the powers of 0,1,2 can make a larger copy of itself. Delian Brick seems like a great name for it. It is a 2-reptile.
https://math.stackexchange.com/questions/2822566/
Graphics3D[{Cuboid[{0, 0, 0}, {2^(0/3), 2^(1/3), 2^(2/3)}], Cuboid[{1, 0, 0}, {1 + 2^(0/3), 2^(1/3), 2^(2/3)}]}]
3D rep-tiles that are not derived from 2D rep-tiles are currently quite rare.
I would not be surprised if this brick was known by the ancient greeks. Has anyone seen it before?
--Ed Pegg Jr _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun