In the Archimedes spiral, the radius from the center increases at a fixed rate as the point, P, moves around the origin. The angle θ also increases, but at a decreasing rate.
The equiangular or Nautilus spiral is a type of spiral that can be found in nature in such things as snail shells. The curve's radius increases at an increasing rate as the point revolves around the origin, but the angle θ always stays fixed—hence the name of the curve. Soon I will hopefully expand this activity with an example of a Euler spiral.