The spiral is made from an infinite series of quarter circles with radii r_{1}, r_{2}, r_{3}, r_{4}, ...

So the length,

The sum of this infinite convergent geometric series is

So

Two semicircles with diameters of Φ & 1 also have a combined length of

So the finite green curve has the same length as the infinite red spiral:

Other equal length spirals are possible:

The blue spiral is made from semicircles whose diameters decrease from 1 in the golden proportion:

Its length is

So :

The purple spiral in this diagram is made from three quarter circles whose diameters decrease in the golden proportion. The initial diameter of two thirds makes the length of this spiral equal to all the other spirals.

The orange spiral in this diagram is made from parts of circles decreased in the golden proportion; about 222° of arc. Again the diameters of these arcs decrease in the golden proportion. The initial diameter of a half of Φ makes the length of this spiral equal to all the other spirals.