The Golden Class

	Take a set of any size elements from one to infinity and index it as the
first in an infinite series of sets. Perform a procedure for producing the next
set in the series based on the prior set. Repeat the process until an adequate
approximation of some golden numbers are found.
	A set of five elements beginning with the first index:

	Set 1: initialize with ones: [1, 1, 1, 1, 1]

The procedure:

Set? of elements: [a, b, c, d, e]

a of set1, or a1; b of set1, or b1; etc.

a1 + b1 + c1 + d1 + e1 = a2
a1 + b1 + c1 + d1      = b2
a1 + b1 + c1           = c2
a1 + b1                = d2
a1                     = e2

Set 1  Set 2  Set 3  Set 4  etc....  Set?
  1      5      15     55             a?
  1      4      14     50             b?
  1      3      12     41             c?
  1      2       9     29             d?
  1      1       5     15             e?

form ratios: ratio1, or r1; ratio2, or r2; etc.

r1 = a?/e?
r2 = b?/c?
r3 = c?/a?
r4 = d?/b?
r5 = e?/d?

form a golden fifth-degree polynomial from these five ratio approximations:

x = r1	  or    x = r2    or    x = r3    or    x = r4    or    x = r5
x - r1 = 0  or  x - r2 = 0  or  x - r3 = 0  or  x - r4 = 0  or  x - r5 = 0
(x - r1) * (x - r2) * (x - r3) * (x - r4) * (x - r5) = 0
x^5 + (-r1 - r2 - r3 - r4 - r5) * x^4 + (

for an even set of elements, such as:

r1 = a?/d?
r2 = b?/b?
r3 = c?/a?
r4 = d?/c?