Whitney Umbrella Views
Loading the math board and drawing, please wait…
This example demonstrates the Whitney Umbrella, a classic self-intersecting surface in 3D space, and explores its shape from multiple viewing angles, highlighting the singular line and cusp structure. Core mathematical concepts include parametric surfaces, singularity theory, self-intersection curves, and 3D geometric visualization. Construction: using GeoGebra's IntersectPath command to compute intersection curves between the surface and auxiliary planes or parameter objects, with objects a, n, p, and eq1 to create dynamic views and allow rotation or slider-based exploration. Suitable for university-level differential geometry, singularity theory, or computer graphics courses as an intuitive teaching aid, and also for advanced high school solid geometry enrichment.
GeoGebra Commands & Parameters
IntersectPath(p, a) → eq1
AI Drawing Prompt Reference
Visualize the Whitney Umbrella in 3D space, highlighting its self-intersecting shape, singular line, and cusp structure from multiple angles, with dynamic views allowing rotation or slider-based exploration by computing intersection curves between the surface and auxiliary planes or parameters.
The prompt above was compiled from the original drawing commands and is for reference only.