A Fermat's spiral or parabolic spiral is a plane curve with the property that the area between any two consecutive full turns around the spiral is invariant. As a result, the distance between turns grows in inverse proportion to their distance from the spiral center, contrasting with the Archimedean spiral (for which this distance is invariant) and the logarithmic spiral (for which the distance between turns is proportional to the distance from the center). Fermat spirals are named after Pierre de Fermat.[1]
Their applications include curvature continuous blending of curves,[1] modeling plant growth and the shapes of certain spiral galaxies, and the design of variable capacitors, solar power reflector arrays, and cyclotrons.
- ^ a b Lekkas, Anastasios M.; Dahl, Andreas R.; Breivik, Morten; Fossen, Thor I. (2013). "Continuous-Curvature Path Generation Using Fermat's Spiral" (PDF). Modeling, Identification and Control. 34 (4): 183–198. ISSN 1890-1328. Archived from the original (PDF) on 2020-10-28.