The ancient Greeks called this target shape a "golden rectangle" because it has the property that the ratio of its width to its height is the same as the ratio of its width plus height to its width. Or if we call its width W and its height H then W/H = (W + H)/W. This equation can be solved to get an explicit expression for the "golden ratio", W/H = (1 + sqrt(5))/2.
This rectangle has many interesting properties and symmetries. For instance, if you divide a golden rectangle into a square of size H and another rectangle, then this new rectangle will also be a "golden rectangle". By repeating this process on each new rectangle you will produce an infinite spiral of squares inside the original rectangle.
The golden ratio and its conjugate, 1 - sqrt(5))/2, are also related to the Fibonacci numbers. The Fibonacci numbers are defined by the following recurrence:
F(0) = 0,
F(1) = 1,
F(k) = F(k-1) + F(k-2) for k ≥ 2
and it can be shown that the terms in this sequence are also given by:
F(k) = (R^k - R_conj^k)/sqrt(5)
where R = the golden ratio and R_conj = the conjugate of the golden ratio.
