A continued fraction can be finite or infinite. One example at right is a finite continued fraction. The other example is an infinite continued fraction. You will need to use the quadratic formula. Prove it if possible.
Golden spirals Construct a golden spiral.
Construct a golden rectangle and the square inside it as before. Inscribe a quarter-circle in the square as shown. In the remaining smaller golden rectangle, make another square. Keep constructing squares and arcs in the smaller golden rectangles that appear. Extensions Consider a golden spiral inscribed in a golden rectangle 1 by g. Find a formula for the length of the nth arc of the golden spiral.