Question

A logarithmic or growth spiral is a special kind of spiral curve. You can distinguish a logarithmic spiral from an Archimedean spiral, because the distances between the turnings of a logarithmic spiral keep increasing, while the distances in an Archimedean spiral are constant. Logarithmic spirals often occur in nature. Select two of the following and explain, using approximate numbers, how the spiral might be logarithmic.

Answer 1

-The approach of a hawk to its prey. As the hawk descends, its best view is at an angle to its flight path; this angle is the same as the spiral's pitch.
-The approach of an insect to a source of artificial light.
-The arms of spiral galaxies. The Milky Way, the galaxy we are in, has several spiral arms.
-The arms of tropical cyclones, such as hurricanes.

Answer 2

Both the example of the hawk and its prey and the Milky Way galaxy are pretty good examples of logarithmic spirals. If you imagine the shape of the trajectory the hawk takes, it is encircling the prey while simultaneously getting closer to it.