“Conchospiral”的意思、由来-开放百科全书

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Conchospiral

释义

Parameterization
History
Applications
References
External links

In mathematics, a conchospiral or conical spiral is a three-dimensional spiral on the surface of a cone.

Parameterization

In cylindrical coordinates, the conchospiral is described by the parametric equations:

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.^[1]

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.^[2]^[3]

References

1. ^{{citation|title=A Monograph of the British Fossil Cephalopoda, Part 1|first=John Frederick|last=Blake|authorlink=John Frederick Blake|publisher=J. Van Voorst|year=1882|page=23|url=https://books.google.com/books?id=aEMYAAAAYAAJ&pg=PA23}}
2. ^{{citation|title=VHF and UHF Antennas|volume=35|series=Institution of Electrical Engineers Electromagnetic Waves Series|first=R. A.|last=Burberry|publisher=IET|year=1992|isbn=9780863412691|page=142|url=https://books.google.com/books?id=6DG09xOjbkMC&pg=PA142|contribution=8.2.4 Conical spiral}}
3. ^{{citation|title=Antenna Theory: Analysis and Design|first=Constantine A.|last=Balanis|publisher=John Wiley & Sons|year=2015|isbn=9781119178989|contribution=11.3.2 Conical spiral|url=https://books.google.com/books?id=PTFcCwAAQBAJ&pg=PA598|page=598}}

External links

{{mathworld|title=Concho-Spiral|urlname=Concho-Spiral}}

1 : Spirals

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