Answer to Question #120198 in Geometry for wayne

Question

Construct a logarithmic spiral using golden rectangles with sides measuring 4 units.

Answer 1

Answer:

The golden rectangle can be constructed with the help of a compass and a ruler:

1) Draw a square with side 4 units.

2) Draw a line through the middle of one side of the square and the opposite vertex

3) Use this line, as a radius, to draw an arc that determines the height of the rectangle

4) Complete the golden rectangle.

$AB=4; BC=2(1+\sqrt{5});$

The golden spiral is composed of consecutive quarters of circles inscribed in each square.