2DCV (Projects): Thomas F. Banchoff (Cervone)


Thomas Banchoff
Influencing
	Davide P. Cervone

GS PD TT

Full Professor
Influences
Graduate Student

Tight Surfaces

Cervone's doctoral thesis studied vertex-minimal and tight immersions of polyhedral surfaces in three-space. In it, he shows that the Klein bottle requires at least 9 vertices for an immersion, and than he produces tight polyhedral immersions of surfaces in homotopy classes for which no examples were previously known.
In subsequent work, Cervone shows that there exists a polyhedral immersion of the real projective plane with one handle, an unexpected result in light of the proof that there is no smooth tight immersion of this surface.
Further work produces two more examples of tight surfaces in new homotopy classes, leaving only one class with no known example (the twisted torus with one handle).

Beyond the Third Dimension

Cervone helped produce the artwork for Banchoff's book, Beyond the Third Dimension: Geometry, Computer Graphics, and Higher-Dimensions, that is part of the Scientific American Science Library series.

Full Professor
Influences
Post-Doctoral Student

StageTools

The StageTools software package is a collection of external modules for the Geomview 3D graphics program. They were designed to make mathematical objects easier to produce, and for creating animations for use on web pages. Work on these programs began during a visit of Banchoff to the Geometry Center in 1994, where Cervone was a postdoctoral student, as a means of producing the movie clips that Banchoff and Cervone wanted for several web-based projects they were working on. StageTools has continued to be developed over the years since then.

Surfaces Beyond the Third Dimension

Banchoff's art show, Surfaces Beyond the Third Dimension, held at the Providence Art Club in the spring of 1996, was created with the assistance of several student associates. Cervone helped produce several of the artworks based on the work he and Banchoff had done together at the Geometry Center.

Full Professor
Influences
Tenure Track
Assistant Professor

Communications in Visual Mathematics

The CVM was a totally electronic journal intended to investigate and develop methods of using hypertext and multimedia approaches to disseminating mathematical research. Banchoff and Cervone produced a prototype issue with several innovative articles that used non-linear organizations and interactivity as an important design consideration.
The CVM is no longer being produced, but it has become part of the MAA's new MathDL digital library project.

Surfaces Beyond the Third Dimension

After the physical art exhibit, Surfaces Beyond the Third Dimension, completed its run at the Providence Art Club, Cervone helped create a virtual art gallery on the web that allows its visitors to explore not just the images themselves, but the mathematics behind them. The virtual show includes animations and interactive versions of the objects it portrays.

Senior Professor
Influences
Tenure Track
Assistant Professor

Math Awareness Month 2000

While president of the MAA, Banchoff proposed "Math Spans All Dimensions" as the theme for Math Awareness Month, April 2000. Banchoff and Cervone designed and produced the poster used for publicising the event, and this poster included an extensive on-line component . This web site allowed visitors to find out more about the individuals who appear on the poster, and about how dimensions play a role in their work.

Para Além da Terceira Dimensão

A physical recreation of Banchoff's 1996 art exhibit, Surfaces Beyond the Third Dimension, as seen in its virtual incarnation on the web , this new art show included not only the printed images, but also continusouly playing video tapes, and computer stations where the visitor could interact with the mathematical objects themselves. This exhibit is a travelling one, and has visited more eight cities in Portugal and Brazil. With its own web site , in both English an Portuguese, several new artworks produced specifically for this exhibit, and a CD-ROM that contains all the artwork and movies in the show, this is a valuable addition to the original Surfaces Beyond the Third Dimension.


Full Professor Influences Graduate Student		Tight Surfaces Cervone's doctoral thesis studied vertex-minimal and tight immersions of polyhedral surfaces in three-space. In it, he shows that the Klein bottle requires at least 9 vertices for an immersion, and than he produces tight polyhedral immersions of surfaces in homotopy classes for which no examples were previously known. In subsequent work, Cervone shows that there exists a polyhedral immersion of the real projective plane with one handle, an unexpected result in light of the proof that there is no smooth tight immersion of this surface. Further work produces two more examples of tight surfaces in new homotopy classes, leaving only one class with no known example (the twisted torus with one handle). Beyond the Third Dimension Cervone helped produce the artwork for Banchoff's book, Beyond the Third Dimension: Geometry, Computer Graphics, and Higher-Dimensions, that is part of the Scientific American Science Library series.


Full Professor Influences Post-Doctoral Student		StageTools The `StageTools` software package is a collection of external modules for the `Geomview` 3D graphics program. They were designed to make mathematical objects easier to produce, and for creating animations for use on web pages. Work on these programs began during a visit of Banchoff to the Geometry Center in 1994, where Cervone was a postdoctoral student, as a means of producing the movie clips that Banchoff and Cervone wanted for several web-based projects they were working on. `StageTools` has continued to be developed over the years since then. Surfaces Beyond the Third Dimension Banchoff's art show, Surfaces Beyond the Third Dimension, held at the Providence Art Club in the spring of 1996, was created with the assistance of several student associates. Cervone helped produce several of the artworks based on the work he and Banchoff had done together at the Geometry Center.


Full Professor Influences Tenure Track Assistant Professor		Communications in Visual Mathematics The CVM was a totally electronic journal intended to investigate and develop methods of using hypertext and multimedia approaches to disseminating mathematical research. Banchoff and Cervone produced a prototype issue with several innovative articles that used non-linear organizations and interactivity as an important design consideration. The CVM is no longer being produced, but it has become part of the MAA's new MathDL digital library project. Surfaces Beyond the Third Dimension After the physical art exhibit, Surfaces Beyond the Third Dimension, completed its run at the Providence Art Club, Cervone helped create a virtual art gallery on the web that allows its visitors to explore not just the images themselves, but the mathematics behind them. The virtual show includes animations and interactive versions of the objects it portrays.


Senior Professor Influences Tenure Track Assistant Professor		Math Awareness Month 2000 While president of the MAA, Banchoff proposed "Math Spans All Dimensions" as the theme for Math Awareness Month, April 2000. Banchoff and Cervone designed and produced the poster used for publicising the event, and this poster included an extensive on-line component . This web site allowed visitors to find out more about the individuals who appear on the poster, and about how dimensions play a role in their work. Para Além da Terceira Dimensão A physical recreation of Banchoff's 1996 art exhibit, Surfaces Beyond the Third Dimension, as seen in its virtual incarnation on the web , this new art show included not only the printed images, but also continusouly playing video tapes, and computer stations where the visitor could interact with the mathematical objects themselves. This exhibit is a travelling one, and has visited more eight cities in Portugal and Brazil. With its own web site , in both English an Portuguese, several new artworks produced specifically for this exhibit, and a CD-ROM that contains all the artwork and movies in the show, this is a valuable addition to the original Surfaces Beyond the Third Dimension.