## The Geometry of the MRB Constant

**Authors:** Marvin Ray Burns

The MRB constant is the upper limit point of the sequence of partial sums defined by S(x)=sum((-
1)^n*n^(1/n),n=1..x). The goal of this paper is to show that the MRB constant is geometrically
quantifiable. To “measure” the MRB constant, we will consider a set, sequence and alternating series of
the nth roots of n. Then we will compare the length of the edges of a special set of hypercubes or ncubes
which have a content of n. (The two words hypercubes and n-cubes will be used synonymously.)
Finally, we will look at the value of the MRB constant as a representation of that comparison, of the length of the edges of a special set of hypercubes, in units of dimension 1/ (units of dimension 2 times
units of dimension 3 times units of dimension 4 times etc.). For an arbitrary example we will use units of
length/ (time*mass* density*…).

**Comments:** 8 Pages. This classic paper shows the utter simplicity of the geometric description of the MRB constant (oeis.org/A037077).

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### Submission history

[v1] 2016-09-06 19:08:36

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