Cubic surface: deformation of Whitneys Umbrella to two A1 singularities @davidamadore
Cubic surface: deformation of Whitneys Umbrella to two A1 singularities  @davidamadore
Uploaded November 2010 | Updated September 2026, 2 weeks ago
A cubic surface with a line of singular points, known as "Whitney's Umbrella", being deformed to one with two A1 singularities. The umbrella occurs at 3ʺ and 9ʺ in the video.

From the cubic surfaces DVD, madore.org/cubic-dvd
Cubic surface: deformation of Whitneys Umbrella to two A1 singularitiesNavigating in a 120-cell (side view, old version)Waves on a flat torus (square lattice)Voronoi cells of the E8 lattice: a three-dimensional cross-section with Coxeter planeCubic surface: deformation of a single A2 singularity (with conjugate planes) to an A1 singularityVisualizing the sphere and the hyperbolic plane: five projections of eachNavigating in a 600-cell (old version)Cubic surface: deformation of an E6 singularity to a D5 singularityThe sound of the Cantor setGrowing circles on a flat torus (square lattice)Poinsot polhodeDeformation of a hexagon with fixed sides and angles
David Madore |

Cubic surface: deformation of Whitney's Umbrella to two A1 singularities

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