MRB Constant

By Marvin Ray Burns

Consider this sequence of n-cubes:

,,,,,,,,,,
… ,

Give each element a content equal
to its dimension. [0]

In the y,z-plane
in 3d space, line up vertically the edge of the Line Segment at the origin down
the z-axis; it stops at the point (0,0,-1). So at the point (0,1,-1) line up an edge of the square so that it stops at the
point (0,1,-1+sqrt[2]). So at the point (0,2,-1+2^(1/2)) line up an edge of the
cube so that it stops at (0,2,-1+2^(1/2)-3^(1/3). Continue stacking an edge of
every hypercube until you get to the cube
of infinite dimension; it starts at the point(0,∞,-m) so that it stops at
the point (0,∞,m) where m is the MRB constant.

[0]

http://www23.wolframalpha.com/input/?i=n-cube

1http://pi.lacim.uqam.ca/fra/table_fr.html

http://pi.lacim.uqam.ca/eng/table_en.html

http://www.irancivilcenter.com/en/tools/units/math_const.php

http://www.wortherkunft.de/~e/c_/ca-zahlen.html

http://free-vz.htnet.hr/nstepan/const/math.txt

http://pi.lacim.uqam.ca/piDATA/mrburns.txt

http://www.research.att.com/~njas/sequences/A037077

S. R. Finch, Mathematical Constants, Cambridge, 2003, pp.
448-452.