Let a, b, c, d, e, f be non-zero integers. Let K be a real number. Consider the equation:

1.0) a/b * k = c/d (given from picture, where a/b = 360, k = Φ ^(-3), c/d=85)
1.1) k = (c/d) * (b/a) (simple algebra)
1.2) k = (cb)/(da) (simple algebra)
1.3) k = e/f (substitution: cb = e, da= f, from closure of integers under multiplication)

Therefore: K is a rational number, since it can be expressed as the quotation of 2 integers (the definition of a rational number).

However Φ ^(-3) is not a rational number.
Therefore: 360 * Φ ^(-3) ≠ 85