The projection of a conchospiral on the plane is a logarithmic spiral.
The parameter controls the opening angle of the projected spiral, while the parameter controls the slope of the cone on which the curve lies.
History
The name "conchospiral" was given to these curves by 19th-century German mineralogist Georg Amadeus Carl Friedrich Naumann, in his study of the shapes of sea shells.[5]
Applications
The conchospiral has been used in the design for radio antennas. In this application, it has the advantage of producing a radio beam in a single direction, towards the apex of the cone.[6][7]
^Burberry, R. A. (1992), "8.2.4 Conical spiral", VHF and UHF Antennas, Institution of Electrical Engineers Electromagnetic Waves Series, vol. 35, IET, p. 142, ISBN9780863412691