Geometry Center Videos, Revisited

Page index: Intro | Written Material: Main Trilogy | Videos: Main Trilogy | Geometry Center Video Library Index

Intro

The trilogy of Geometry Center videos are now all legally available for free online! These videos brought brought concepts from geometric topology to general audiences through computer-generated visualization in the early 1990s. Not Knot, released in 1991, illustrates a remarkable swath of knot theory and hyperbolic geometry. Outside In, released in 1994, showcases Thurston's approach to turning a sphere inside out. The Shape of Space, finished in 1995, is about spaces that are finite but have no boundaries, covering some of the material in the book of that name by Jeff Weeks. These videos were shown at the SIGGRAPH Electronic Theater, featured on the cover of Scientific American, and won awards at NICOGRAPH, the London Effects and Animation Festival, Prix Pixel Imagina, and Prix Ars Electronica.

These creations are no longer formally in print, since VHS tapes and DVDs are obsolete. The rights have now been reverted from the original publishers (AK Peters and Key Curriculum Press) to the authors. We are now able to post both the videos and written supplements for all to enjoy. The videos have been uploaded by many people over the years and viewed many millions of times (and even used for parody mashups!), but the written supplements had not been widely available.

In addition to the flagship videos, many more videos were created at the Geometry Center by visitors and summer interns, typically made in collaboration with the technical staff. Some were fully scripted and narrated videos that can stand alone. Others were intended as "video overheads", made to accompany a research talk given by a mathematician - quick to create, and without voiceovers. Many documented summer student projects. Over 200 physical videotapes were created, using a mix of single-frame recording and live on-screen demos. We are now digitizing and uploading most of the unique (finalized, non-draft) material that was the core of Geometry Center video library; the full list of what has been / will be converted is below.

The Geometry Center was the short name of the NSF-funded National Science and Technology Center for the Computation and Visualization of Geometric Structures, which was located at the University of Minnesota from 1991-1998. Its precedessor, The Geometry Supercomputer Project, started in 1987. Video creation was only one of the many achievements of the Center; a good overview of the full scope of its mission and accomplishments is in the 1994 self-study report.

Written Material: Main Trilogy

High quality scans
- Supplement to Not Knot by David Epstein and Charlie Gunn (50 pages, black & white, 12MB)
- Making Waves: A Guide to the Ideas behind Outside In by Silvio Levy (50 pages, full color, 20MB)
- Exploring The Shape of Space by Jeffrey R. Weeks (150 pages, black & white, 23MB)
  - Free accompanying software: Torus Games runs on iOS, Android, Windows and Mac
Books
- The Shape of Space, 3rd edition, Jeffrey R. Weeks, CRC/Routledge
- Three-Dimensional Geometry and Topology, Vol. 1, William P. Thurston and Silvio Levy, CRC/Routledge

Videos: Main Trilogy

Not Knot, 17 min
- Not Knot HD: upscaled from original 480p to 1440p by LastGinger, 13K views
  - Many links to more resources on that page, including Not Knot full credits text
- Not Knot full upload from Danny, 32K views
- The Geometry Center Presents Not Knot full upload from Alec Jacobson, 8K views
- Not Knot direct upload of remastered DVD from me
Outside In, 22 min
- Outside In HD: upscaled from original 480p to 1440p by LastGinger, 110K views
  - Many links to more resources on that page, including Outside In full credits text
- Outside In full upload from ssgelm, 5M views
- how to theoretically turn a sphere inside out partial upload (10 min) from speedysatliteguy, 6M views
- Sphere Inside out Part - I Outside In first half (10:30) from akhileshpathak, 920K views
- Sphere Inside out Part - II Outside In second half (10:50) from akhileshpathak, 2M views
- How To Turn A Sphere Inside Out Outside In Scene 1 (1:40) from Davies Robinson, 40K views
- Outside In, Excerpts 1 Outside In Scene 1 (1:25) from me, 3K views
- Outside In, Excerpts 2 Outside In Other Scenes (3:18) from me, 3K views
- Outside In original direct upload from original D1 master used to create DVD, from me
- How to turn a sphere inside out but every time they say "sphere" or "circle" it gets faster title says it all... from PLAP CAST, 154K views
- [YTP] OUTIE INNIE OUCHIE, Outside In mashup from cs188, 417K views
- {YTP} Phere Seversion (Collab Entry) Outside In mashup from YAPfNY, 23K views
- Thurston corrugation eversion video by Carsten Steger (2 min, sphere eversion wikipedia)
The Shape of Space, 11 min
- The Shape of Space original, direct upload from original D1 master used to create DVD, from me, 19K views
Views counts above are from October 2021

Geometry Center Video Library Index

Compilations
- M-08: 1991 Summer Student Compilation 16.9 min (Mangled audio: timecode audible on audio track.)
  - 0:58-1:06 "Geometry Center Summer 1991 Student Projects, Video Supplement"
  - 1:06-1:24 Geometry Center intro.
  - 1:24-2:15 Adrian Mariano. Parallel Curves and Caustics. Parallel Curves to an Eclipse.
  - 2:15-2:50 Adrian Mariano, Self-Parallel Curve
  - 2:50-3:28 Adrian Mariano, Caustics to a Circle.
  - 3:28-4:36 Caustics to an Eclipse (A.M.)
  - 4:36-5:38 Parallel Surfaces to an Ellipsoid (A.M.)
  - 5:38-7:52 David Broman. Demonstration of Linktool.
  - 7:52-8:38 Adam Halvorsen. A Quick Dissection of the Fourth Dimension. Truncated Hypercube/Octaplex.
  - 8:38-9:00 Stellaoctangula from Hypercubes.
  - 9:00-9:25 Henry Rowley. Isometric Deformations of Surfaces. Rectangle to a Cylinder.
  - 9:25-9:40 Sector of a Circle to a Cone. Henry Rowley.
  - 9:40-10:21 Catenoid to a Helicoid. Henry Rowley.
  - 10:21-10:59 Rectangle to a Moebius Strip. Henry Rowley.
  - 10:59-11:30 Arek Goetz. Midpoint Transformation of Polygons.
  - 11:30-11:41 Transformation to an Ellipse. Arek Goetz.
  - 11:41-12:12 Kenneth Bromberg. Bisection Envelopes.
  - 12:12-16:18 Linus Upson. Flying in Hyperbolic Space.
  - 16:18-17:22 Mike Huberty. CEM-ECM Logo and Curve Shrinking.
  - 17:22-17:51 Ending Credits: "This video was Directed and Produced by Adrian Mariano and Henry Rowley (in 2 days)...."
- M-28: 1991 Compilation
  - Geometry & the Imagination leader (Maxwell)
  - Geometry & Imagination lectures (Thurston, Conway, Doyle, Gilman)
  - Student Project: Rolling cube (Rowley)
  - Student Project: Caustics/parallel surfaces (Mariano)
  - Student Project: Hyperbolic flight (Upson)
  - Student Project: LinkTool (Broman)
  - Student Project: ECM/CEM in octagons (Huberty)
  - Sphere Eversion (Ben-Zvi & Headrick)
  - Polyhedral Treasure (Holt)
- M-30: Animated Geometry: Student Video Projects Summer 1992
  - Kate Jenkins, Lindenmayer Systems and Plant Development
  - Stephanie Mason, Lindenmayer Systems and Space-Filling Music
  - Thomas Colthurst, Fractal Polytops and Equivalent IFS's
  - Nick Coult, Special 3-Body Systems
  - Jacques Friedman, The 3-ring Circus: A Conservative Dynamical System
  - Mark Meloon, Nonlinear Control and the Inverted Pendulum Problem
  - Linus Upson and Adrian Mariano, Penumbral Shadows
  - Ken Bromberg, A Minimal Surface in Hyperbolic Space
  - Gary Gutman, Rolling Up a Two-Holed Torus
  - David Broman, Linktool 2.0
  - Chris Cianflone, Experiments in Computer Music
  - Craig Sutton, SO3: It's Fundamental
  - Jennifer Ellison and Sherry Scott, Groups of Symmetry
  - Prem Janardghan, Karen Olsson, Carol Sohn, The Shape of Space
- M-53: Interesting 91-92-93
  - 00:14 - 10:20. Charlie Gunn, Exploring Hyperbolic Space Using Geomview. 10.5 min
  - 1:25 - 17:25. Richard Morris, A Parade of Surfaces. 6.5 min
  - 17:30 - 28:30. John Maddocks, MC^2: Multiplier and Constraint Continuation. 11 min.
  - 28:30 - 38:00. Leonidas Palios and Mark Phillips, Tetrahedral Breakup. 9.5 min.
  - 38:00 - 45:55. Dennis Roseman, Viewing Knotted Spheres in 4-Space. 8 min.
  - 46:00 - 53:30. Alfred Gray, Strange Surfaces. 8 min.
  - 53:30 - 1:08:25. 1992 High School Mentoring Compilation. 14 min.
  - 1:09:00 - 1:21:30. Celeste Fowler, Shape of Space. 13 min.
  - 1:21:40 - 1:24:25. Olaf Holt, Dance of the Platonic and Archimedean Solids. 3 min.
  - 1:24:30 - 1:34:15. Bruce Peckham, Resonant Surfaces. 10 min.
  - 1:34:15 - 1:37:25. John Lowengrub, Vortex Sheet With Surface Tension. 3 min.
  - 1:37:30 - 1:43:00. Charlie Peskin & Steve McQueen, Heart animation. 6 min.
- M-61: Quick Cuts from the Geometry Center Compilation 1993
  - 00:15 Beginning Credits
  - Staff
    - 00:36. Outside In. Center Staff
    - 00:53. 4D Hypercube Rotation. Olaf Holt
    - 01:31. Exploring Hyperbolic Space Using Geomview. Charlie Gunn
    - 02:33. Shape of Space. Celeste Fowler
    - 03:20. Dance of the Platonic and Archimedean Solids. Olaf Holt
  - Students
    - 05:45. Rolling Cube. Henry Rowley
    - 06:04. Vibrating Evolved Minimal Surfaces. Jeremy Ackerman
    - 06:25. School. Maria Nagan
    - 06:59. The Complex Henon Map. Brian Meloon
    - 07:37. The Diving Simulator. Elizabeth Callaghan
    - 08:22. Slicing the Cubic Connectedness Locus. Christine Heitsch
    - 09:08. SO3: It's Fundamental. Craig Sutton
    - 10:28. Lindenmayer Systems and Plant Development. Kate Jenkins
    - 11:23. Penumbral Shadows. Linus Upson, Adrian Mariano
  - Visitors
    - 13:15. Heart Animation. Charlie Peskin, Steve McQueen
    - 13:34. 3D Crystal Growth. Ryo Kobayashi
    - 14:02. Anisotropy in Diffusion Limited Aggregation (DLA) and in Modified DLA. Bayard Johnson, Robert Sekerka
    - 14:41. Classical Surfaces. Alfred Gray
    - 15:04. Simulation of Crystal Growth Using Fully-Facetted Interfaces. Andy Roosen
    - 15:26. Twisting and Turning in Four Dimensions. Dennis Roseman
  - Geometry Supercomputer Project, 1989-1991
    - 18:20. Not Knot. Gunn, Maxwell, Levy, Orloff
    - 19:11. Rotating Soap Bubbles. John Sullivan
    - 19:28. Soap Bubbles With Procedural Shading. John Sullivan, Pat Hanrahan
    - 19:47 Good Fibrations: Visualizing the Hopf Fibration. Mark Goldman, Mark Phillips
    - 20:33. Potential Energy vs. Bond Length for H2S. Toby Orloff, Laurie Butler
    - 20:59. The Cubic Connectedness Locus. Charlie Gunn
    - 21:25. Moebius Band with Circular Boundary. John Sullivan, Cary Sandvig
    - 21:44. Dirichlet Domains for Low Volume Hyperbolic Manifolds. Charlie Gunn
    - 21:58. Crossing External Rays of the Mandelbrot Set. Adrien Douady, Rene Adad, Charlie Gunn
  - 22:50. End Credits
  - 23:02. End
  - edited by Tamara Munzner
- M-67: Animated Geometry II: Student Video Projects Summer 1993
  - 0:00. Introduction and Credits
  - 0:31. Ackerman, Jeremy. Vibrating Evolved Minimal Surfaces. 2:43
  - 3:39. Bancroft, Kirsten. Circulatory System Animation. 2:00
  - 5:36. Callaghan, Elizabeth. The Diving Simulator. 3:33
  - 9:16. Chin, Sang. Visualizing the Weierstrass p-function. 3:16
  - 12:01. Coult, Nick. The Solar System Viewer. 3:20
  - 15:22. Duvall, Danek. Clouds. 1:50
  - 17:16. Friel, Patrick. Mazes and Meanders. 2:47
  - 20:03. Heitsch, Christine. Slicing the Cubic Connectedness Locus. 3:24
  - 23:19. Jenkins, Kate. Binary Trees and Ray Tracing. 3:58
  - 27:08. Leonard, Heather and Rowley, Timothy. Northern Exposure. 2:10
  - 29:25. Li, Jing. Tonality Circles. 3:05
  - 32:24. Meloon, Brian. The Complex Henon Map. 2:15
  - 34:15. Niss, Millie. The Sphere Scribbler. 3:20
  - 37:33. Parekh, Hiren. Conformal Embeddings in 3-Space. 2:55
  - 40:29. Sullivan, Michael. Singular knots for "Linktool". 3:38
  - 44:15. Van Der Werf, Deva. The Teichmüller Navigator. 2:30
  - 46:21. Wade, Dan. Spiderwebs. 3:55
  - 50:16. Dunn, Brendan. Networks of Neurons. 15:22
  - Ending Credits
  - Editors: Daeron Meyer, Nathaniel Thurston
- M-75: Animated Geometry III: 1994 Undergraduate Summer Institute Videos
  - 00:00. Introduction and Credits
  - 00:22. Geodesics on Surfaces. Don Barkauskas
  - 04:11. Backing up a Trailer. Li-Tien Cheng
  - 06:29. Geodesics on Orbifolds. Yevgeniy Dodis
  - 10:55. Solving Quintic Polynomials. Eric Egge
  - 15:37. Visualizing Subgroups of SU(2). Rebecca Frankel
  - 18:53. Visualization of Higher Dimensions. Brian Luense
  - 23:40. Computer Visualization of Soap Films. Luke Meyer
  - 27:15. Dynamics of Josephson Junctions. Mike Pelsmajer and Liz Stanhope
  - 32:22. Collision Detection for Surface Evolver. Jovan Popovic
  - 36:07. Ant Trails. Kim Retert
  - 39:43. Visual Genetic Programming. Tim Rowley
  - 43:29. Seifert-Weber and Poincare Dodecahedral Spaces. Nicole Young
Individual Tapes (entire tape uploaded as single segment)
- M-51: Voyager from the Fourth Dimension, Olaf Holt & Paul Humke. 6 min
- M-86: Mad About Mirrors, Anna Gardberg. 6.5 min
- M-73: Computer Visualization of Bifurcation Phenomena, Richard McGehee and Rick Wicklin and Nicholas Vera. 14.5 min
- M-82: My time at the Geometry Center, Chaim Goodman-Strauss, Aug 14, 1995. 84 min
- M-85: Geometry... The Next Generation, Lori Holthus. 8 min
- M-90: Viro's Patchworking Disproves Ragsdale's Conjecture, Jesus de Loera and Rick Wicklin, June 1997. 8.5 min (Audio missing.)
- S-02: Complex Hyperbolic Space, William Goldman, Robert Miner, Mark Phillips. 12.5 min
- S-23: Limit Sets of Kleinian Groups, Mandelbrot Set, Dirichlet Domains for Low Volume Hyperbolic Manifolds. 8.5 min
  - David Mumford and David Wright, Limit Sets of Kleinian Groups
  - Rene Adad and Stuart Levy, Crossing a Filament of the Mandelbrot Set
  - Charlie Gunn, Dirichlet Domains for Low Volume Hyperbolic Manifolds
- S-25: Charlie Gunn, trigrp, linkmover, dirdom demos. 6.5 min
- S-114: SaVi: A Program for the Visualization of Satellite Constellations, Bob Thurman & Patrick Worfolk. 6 min
- S-116: Genesis Mission for JPL -- FINAL Nov 10, 1996 -- Lori Thomson & Stuart Levy. 9 min. (Audio missing)
- S-119: Segmentation through the Riemannian Evolver, Tony Yezzi & Allen Tannenbaum. 15 min
- E-1: Mathematical Visualization Through Video, Tamara Munzner. SIGGRAPH 1995 Tutorial on Visualizing Mathematics. 14.5 min
- E-2: Visualizing the Invisible, Tamara Munzner & Al Marden. 44 min
  Video footage for 1994 talk given at Weisman Museum of Art (Minneapolis MN) and Minnesota Council of Teachers of Mathematics Spring Meeting (Brainerd MN).
  - 00:00 Section - Intro
  - 00:01 Dance of the Platonic & Archimedian Solids, Olaf Holt
  - 01:15 A Zoom into the Mandelbrot Set, Charlie Gunn & Matt Grayson
  - 01:53 Geomview: Kuen's Surface, Alfred Gray
  - 02:27 Geomview: Kelvin Counterexample (dodecahedral tiling), Denis Weaire & Robert Phelan
  - 03:02 Heart Animation, Charlie Peskin & Steve McQueen
  - 04:41 Soap Bubbles With Procedural Shading, John Sullivan & Pat Hanrahan
  - 05:29 A Diving Simulator, Elizabeth Callaghan
  - 06:28 Section - Graphics
  - 06:32 Luxo Jr, Pixar
  - 08:45 Building a better dinosaur poster, Silicon Graphics
  - 09:14 Geomview flythrough of office dataset side by side with camera frustum
  - 10:01 blue & yellow striped plane to show perspective distortion
  - 10:28 Section - Dimension
  - 10:34 Cube & 4D Hypercube Rotation, Olaf Holt
  - 14:28 Twisting and Turning in Four Dimensions, Dennis Roseman
  - 15:40 5-Cube, Olaf Holt; QuasiTiler, Eugenio Durand & Stuart Levy
  - 17:51 Section - Hyperbolic Geometry
  - 17:56 Dirichlet Domains for Low Volume Hyperbolic Manifolds, Charlie Gunn
  - 18:45 Geomview interactive demos: Hinge, Mark Phillips; Triangle Tilings, Charlie Gunn, Hyperbolic Dodecahedral Tilings, Charlie Gunn & Tamara Munzner
  - 23:58 Not Knot excerpt: Hyperbolic Dodecahedral Tilings
  - 28:22 Pleated Surfaces, Conformal & Projective Models of Hyperbolic Space
  - 30:38 Section - Math is Everywhere
  - 35:10 Outside In excerpt
- Triangle Tilings. Science Museum of Minnesota / SIGGRAPH 1994. Interactive SGI software from The Geometry Center. 10.75 min
Segments (separate segments uploaded from specific tapes)
- S-33: 14.5 min
- S-51: 61 min
- S-52 76 min
  - Sphere Eversion, Ben-Zvi/Headrick, edited & narrated. Audio mangled. 6.5 min
  - Three Dimensional Crystal Growth. Ryo Kobayashi & Stuart Levy. 2.5 min
  - The Projective Plane, a Seamless Coat Sewn from Three Patches. Jim Cobb & Herb Clemens. 9 min
  - Algebraic Curves. Audun Holme & Joel Roberts. Animation & live whiteboard video. Voiceover mangled. 24 min
  - Tetrahedral Breakup. Leonidas Palios and Mark Phillips. 9.5 min
  - Fugue for Polyhdra in B-flat Major: The Platonic and Archimedean Solids rotating about the 2,7 Torus Knot. Olaf Holt. Audio mangled (music mixed with timecode). 3 min
- S-62
  - Mark Phillips, The Double Torus Unfolded. Video recording of movie made at GE R&D in summer of 1984. 1.2 min.
- S-69:
  - Resonant Surfaces, Bruce Peckham. 10.5 min. Audio mangled.
  - Vortex Sheet With Surface Tension. Thomas Y. Hou, John S. Lowengrub, Michael J. Shelley. 6 min
- S-70:
  - Classical Surfaces, Alfred Gray. 17 min
    - 00:10 Astrotoroidal Sphere
    - 00:44 Bohemian Dome of Type (4,4,4)
    - 01:23 Bohemian Dome of Type (8,3,3)
    - 02:00 Catenoid
    - 02:39 Constant Positive Curvature Surface of Revolution of Barrel Type
    - 03:18 Constant Positive Curvature Surface of Revolution of Football Type
    - 03:55 Crosscap
    - 04:36 Dini's Surface of Constant Negative Curvature (A Generalized Helicoid)
    - 05:19 Ellipsoid Showing Lines of Curvature
    - 05:53 Enneper's Minimal Surface
    - 06:33 Helicoid
    - 07:11 Henneberg's Minimal Surface
    - 07:49 Hyperboloid of Two Sheets Showing Lines of Curvature
    - 08:25 Klein Bottle
    - 09:25 Kuen's Surface of Constant Negative Curvature
    - 10:15 Monkey Saddle
    - 10:54 Pseudosphere
    - 11:33 Conoid
    - 12:08 Steiner's Roman Surface
    - 12:54 Ellipsoid Parametrized by a Generalized Stereographic Projection
    - 13:32 Torus of Type (4,4,4)
    - 14:00 Torus Type (3,8,8)
    - 14:33 Torus Knot of Type (2,5)
    - 15:18 Twisted Sphere or Corkscrew Surface
    - 15:56 Catalan's Minimal Surface
  - Quasicrystal Sculpture for Denmark's COAST. Tony Robbin. 2.5 min
- S-86:
  - Knots Minimizing a Moebius-Invariant Energy, John Sullivan, Nov 1993. 6.5 min
  - Algorithm Animations, George Havas. Jan 1994. 28 min.
- S-98:
  - Computing Periodic Delone Tilings. Daniel Huson. July 1994. 4.25 min
- S-102:
  - Symmetric Frameworks, Bob Connelly & Allan Back. 4.5 min
- S-103:
  - The Geometry and Topology of the Costa Surface. Bogdan Butoi, Victor J. Donnay, Stuart Levy, Tamara Munzner, Mihaela A. Teodorescu. Bryn Mawr for Maryland Science Center. 4.75 min
- S-106:
  - 1/2/4/7: Tom Banchoff, Flat torus rotations etc with software "fourd".
  - 3: 01:23 - 05:30. Complex function graphs: (with Davide Cervone) (live recording). Hypercube alone; w = z^2; w = z^3; w = e^z. Narrated (on the fly!) by Tom Banchoff. Audio manglged.
  - 5: 07:00 - 11:30. Visualization of Hop Dynamics in the 3-Body Problem. Ed Belbruno with Stuart Levy. Initial audio mangled, then cuts off.
  - Skew Polyhedra, Heidi Burgiel & Stuart Levy. May 9, 1995.
  - Calculus lecture animations, Scot Adams, U Minnesota Math Dept, June 1995. 1 min
  - 10: 20:00 - 23:15 Hop Dynamics in the Comet Oterma, Ed Belbruno, June 1995. Initial audio mangled, then cuts off.
- S-113:
  - My Time at the Geometry Center Part 2. Chaim Goodman-Strauss. Spirographs, Dodecafoam, Stellated Icosahedra. Aug 1995
  - Some Radially Symmetric and Non-Radially Symetric Profiles. Doug Clancey, Project Afton. Dec 1995. 2.3 min
  - Mission: Invariant! Peter Olver, Steven Haker, Allen Tannenbaum, & Stuart Levy. June 1996. (curve-shortening flows applied to feature recognition). 2.5 min
  - Glimpses of the Five Platonic Solids. Gabor Toth (Rutgers, Camden) & Stuart Levy. July 1996. 10.5 min
  - 24:30 - 28:00. Tony Yezzi, Allen Tannenbaum. Segmentation through the Riemannian Evolver. March 5-6, 1997. With slevy.
  - 3-Dimensional Competitive Lotka-Volterra Systems. Michael Drew Lamar, Stuart Levy, Mary Lou Zeeman. May 1997. 2.8 min
  - Hydroturbine Blades and Water Passages. Dmitry Gokhman, Stuart Levy, Michael Drew LaMar, Mary Lou Zeeman.
- S-115:
  - Petrie-Coxeter Polyhedron. Heidi Burgiel. 6 min
- S-117:
  - Honeywell Missile-Target Pursuit Animation, Nicholas Vera and Mark Phillips, Dec 1996. 8.5 min

Tamara Munzner

Last modified: Tue Jan 11 02:08:27 PST 2022