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| Dürer's constaruction
of the Archimedean Spiral Albrecht Dürer (1471-1528), the famous Renaissance painter,
printmaker, engraver, mathematician, and theorist,
presented a drawing with a detailed method for the
construction of spirals (Schneckenlinien). He
published it in 1525 in the first book of his treatise >Underweysung der messung, mit
zirckel und richtscheyt< (Teaching of
Measuring).
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| Archimedean | Logarithmic | |
| Polar equation: |
r(φ)
= a · φ a constant |
r(φ)
= exp(a·φ)
a constant
|
| Parameter form: | x
= φ · cos(φ) y = φ · sin(φ) |
x = exp(a·φ)
· cos(φ) y = exp(a·φ) · sin(φ) |
Property
of the Archimedean spiral:
successive turnings have a constant separation distance.
Property
of the Logarithmic spiral:
the
angle θ between the tangent and
radial line at the point (r,φ) is constant, and
equal to arctan(1/a).
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|
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Albrecht Dürer (MacTutor History of Mathematics archive) Albrecht Dürer: Underweysung
der Messung, mit dem Zirckel und Richtscheyt Archimedean
spiral (Wikipedia) Logarithmic spiral (Wikipedia) Spiralen ("Schneckenlinien") bei Albrecht Dürer (TU Freiberg) |
| Books |
| Albrecht Dürer:
Unterweisung der Messung, Faksimile Neudruck der Ausgabe
Nürnberg 1525, Verlag Dr. Alfons Uhl, Nördlingen 2000. |
Updated:
2023, Oct 06
©
2011-2023 J. Giesen
