Math 6

This math issue is based on the next video: https://www.youtube.com/watch?v=7lRgeTmxnlg

 

Many people know or are familiair with the golden ratio which appears via de fibonacci series:

 

0 1 1 2 3 5 8 13 ect

 

there the math sequcne is 

Pn= P(n-1) + P(n-2)

 

there is seemingly a guy (see the video) who invented the silver ratio:

in which defined by:

 

Pn= 2* P(n-1) + P(n-2) 

 

Now lets us generalize this even wider:

 

Pn = X* P(n-1) + Y* P(n-2) in which X and Y are arbitrairy whole numbers positive or negative (one can ALSO extent this to any number for X and Y including the irrational ones the natural one, divisions, imaginairy etc) but lets keep it relative simple here, for now. 

 

And one may already catch the drift, then it is possible to construct a 3D graph where X and Y are being put on respectivily the X and Y axis and the outcome is the precious materials-series on the Z axis (Z0, Z1, Z2 etc) for every in dividual combination.

 

of course of any of these combinations you can calculate the ratio between the former and the latter the higher i in Zi becomes. This obviously leads to an infinity amount of ratios. 

 

The general Idea is worked out in the next excel sheet:

Precious Materials Series
Excel – 14,6 KB 74 downloads

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