[seqfan] Re: Higher dimensional analogues to plane division by ellipses?

[Hans Havermann]

For those of you (like me) who haven't encountered the expression 'Metallic Means' before, this appears to be a 1999 designation created by Buenos Aires mathematician Vera W. de Spinadel to extend the 'Golden Mean' concept < http://www.mi.sanu.ac.rs/vismath/spinadel/ >. The 'silver ratio' [1+sqrt(2)] seems to be a better known example. Ukrainian computer scientist Alexey Stakhov, author of 'The Mathematics of Harmony' (2009), mentions it in section 4.2 < http://peacefromharmony.org/docs/7-27_Stakhov_Math_of_Harmony_EN.pdf >. I assume Koshy refers to Thomas Koshy who authored 'Fibonacci and Lucas Numbers with Applications' (2001).


On Jun 1, 2013, at 5:35 AM, Jess Tauber <yahganlang at gmail.com> wrote:

>> The (2,1)-sided version of the Pascal Triangle appears to be special in at
>> least this- diagonal values are identical to numerical coefficients of
>> power terms that sum to powers of Metallic Means (and the dimensional
>> labels of the diagonals are the same as the powers the terms are raised
>> to)- I worked this out about a year and a half ago and still haven't yet
>> found out if this is an old result, though some work by Koshy appears to
>> suggest it is known).