Number Theory

    

Observations on Zeta(3) from Piling Cubes

Authors: Brian Scannell

We look here at the geometry of zeta(3). By piling cubes a 3D shape is defined which has a volume of zeta(3). This shape is a double integral form for zeta(3). Considering the centroid of this shape leads to an experimental estimate for zeta(3). Cutting the shape parallel to the x axis reproduces the dilogarithmic relationship to zeta(3). Cutting the shape in the z axis reproduces the logarithmic version of Riemann’s formula for zeta(3). Geometrical considerations also reproduce formula for the polylog of a half Lin(1/2) for n=2 and 3. These are illustrations of number geometry.

Comments: 28 Pages.

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Submission history

[v1] 2016-03-30 18:19:23

Unique-IP document downloads: 402 times

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