section_path: Writings/Surviving works/On Spirals
section_name: On Spirals
paragraph_text: On Spirals
  
  This work of 28 propositions is also addressed to Dositheus. The treatise defines what is now called the Archimedean spiral. It is the locus of points corresponding to the locations over time of a point moving away from a fixed point with a constant speed along a line which rotates with constant angular velocity. Equivalently, in modern polar coordinates (r, θ), it can be described by the equation r = a + b θ {\displaystyle \,r=a+b\theta } with real numbers a and b.
  
  This is an early example of a mechanical curve (a curve traced by a moving point) considered by a Greek mathematician.