Wolfram Demonstrations Project

13,000+ Open Interactive Demonstrations
Powered by Notebook Technology »

Helicoid with a Hole

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

Obtained in terms of elliptic functions [2], this minimal surface has two helicoidal ends consisting of a helicoid with a hole and handle; it has genus one and it is invariant under a one-dimensional group of translations.

Contributed by: Enrique Zeleny (June 2014)
Based on a program by: Paul Nylander
Open content licensed under CC BY-NC-SA

Snapshots

Details

References

[1] D. Hoffman, H. Karcher, and F. Wei. "The Genus One Helicoid and the Minimal Surfaces that Led to Its Discovery in Global Analysis and Modern Mathematics." (1993) www.gang.umass.edu/preprint/documents/gang3-16.pdf.gz.

[2] M. Weber. "The genus One Helicoid as a Limit of Screw-Motion Invariant Helicoids with Handles." (Jan 6, 2003) www.indiana.edu/~minimal/research/heliclay.pdf.

Embed Code

Take advantage of the Wolfram Notebook Emebedder for the recommended user experience.

Related Demonstrations More by Author
Browse all topics
Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send