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A logarithmic spiral differs from an Archimedean spiral in that its radius

  • A.increases in geometric rather than arithmetic progression
  • B.increases in arithmetic rather than geometric progression
  • C.remains constant as the angle increases
  • D.decreases as the angle increases from the pole

Answer: A

Correct answer: increases in geometric rather than arithmetic progression

In an Archimedean spiral equal angles add equal increments to the radius; in a logarithmic spiral they multiply it by a constant factor, so the turns spread further apart as the curve grows. The logarithmic form is self-similar under scaling, which is why it appears in shells and in the profiles of certain cams and cutters.

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