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In Proceedings of Bridges: Mathematics, Art, Music, Architecture, Culture

Approximating Logarithmic Spirals by Quarter Circles

Ulrich Reitebuch, Martin Skrodzki, and Konrad Polthier

An approximation of a logarithmic spiral, build from “better golden rectangles” and its reparametrization to an approximate golden spiral. The right image also includes a copy of the reparametrization, rotated by 𝜋.

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The approximation of a golden logarithmic spiral by quarter circles is well known. Starting from this, we show that any logarithmic spiral can be approximated by quarter circles in a similar way. Using our construction on a rectangle with aspect ratio √𝜙 and performing a coordinate reparametrization, we obtain an aesthetic partition of the plane as our main artwork.

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Ulrich Reitebuch, Martin Skrodzki, and Konrad Polthier, Approximating Logarithmic Spirals by Quarter Circles, In Proceedings of Bridges: Mathematics, Art, Music, Architecture, Culture, pp. 95–102, 2021.

BibTex 

@inproceedings{bib:reitebuch:2021,
    author       = { Reitebuch, Ulrich and Skrodzki, Martin and Polthier, Konrad },    
    title        = { Approximating Logarithmic Spirals by Quarter Circles },
    booktitle    = { In Proceedings of Bridges: Mathematics, Art, Music, Architecture, Culture },
    editors      = { Swart, David and Farris, Frank and Torrence, Eve },
    year         = { 2021 },
    pages        = { 95--102 },
    publisher    = { Tessellations Publishing },
    organization  = { Bridges },
    address      = { Phoenix, Arizona },
    url          = { https://publications.graphics.tudelft.nl/papers/337 },
}