TOPICS
Search

Daisy Surface

DOWNLOAD Mathematica NotebookDownload Wolfram Notebook
DaisySurface

The daisy surface is the sextic surface

(x^2-y^3)^2=(z^2-y^2)^3,
(1)

named by Hauser. It is distinct from the spiral-based daisy construction. Its singular points form the set

{(x,y,z):x^2=y^3, z^2=y^2},
(2)

which consists of two curves with cusps in the planes z=y and z=-y. They have parametric equations

x=t^3
(3)
y=t^2
(4)
z=+/-t^2.
(5)

The two curves meet only at the origin and have distinct tangent lines there. Their behavior makes the daisy surface a useful example in resolution of singularities (Faber and Hauser 2010, pp. 406-411).

See also

Cusp, Resolution of Singularities, Sextic Surface

Explore with Wolfram|Alpha

References

Faber, E. and Hauser, H. "Today's Menu: Geometry and Resolution of Singular Algebraic Surfaces." Bull. Amer. Math. Soc. 47, 373-417, 2010. https://doi.org/10.1090/S0273-0979-10-01295-4.Hauser, H. "Gallery of Singular Algebraic Surfaces: Daisy." https://homepage.univie.ac.at/herwig.hauser/gallery.html.

Cite this as:

Weisstein, Eric W. "Daisy Surface." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DaisySurface.html

Subject classifications