External links

[Keiji]

I have copied Alkaline's list of links here, into one page rather than lots. Feel free to reply to suggest new links to add to this list, but I will delete your post after adding it to keep it tidy.

Fourth Dimension: Tetraspace (Garrett Jones)
Higher Dimensions Database (Team Ikaria)

Short introductions
Beyond 3D: Introduction to the Fourth Dimension (Davide Cervone)
Bogglers: Hyperspace: Up, Out, and Away (Discover Magazine)
Dimensions (The Tesseract School) - hypercubes up to the seventh dimension
Dimensionality (Dwight Vincent) - a discussion involving the history of dimensionality
E. Mayev's Fourth Dimension (Emil Mayev)
Fourth Dimension Simply Explained (University of Virginia) - collection of essays submitted to a contest to describe the fourth dimension in under 2500 words
Higher Dimensions (Lee Stemkoski)
Hypercube (Drew Olbrich) - sequence of images showing the rotation of a hypercube
Hypercube (also in German) (Juergen Koeller) - drawings, coordinates, and equations of the hypercube
Hypercubes (Jonathan Bowen) - introduction to n-dimensional objects
An Introduction to the Fourth Dimension and Beyond (Gerald Clement St. Germane) - introduces hypercubes, has a table of geometric properties of structures from the 1st to the 13th dimension, and gives the properties of multi-dimensional rectangular structures
On the Fourth Dimension (James McManus)
Topology and Juggling: Four-Dimensional Braids (Brown University) - uses juggling to demonstrate four dimensional braids
Understanding Dimensions (Vivek Panda) - discussion on time flow rate, curved space, and virtual present
What is the Fourth Dimension? (Rick Duval)
Why Bother with Extra Dimensions? (Sanjeev Seahra) - history of the fourth dimension in science, dimensionality and unification of time and space, gravity and magnetism, fundamental forces

Visualization
Viewing Four-Dimensional Objects In Three Dimensions (Geometry Forum)
Visualizing 4 dimensional objects in 3 dimensional space (Gurudev) - introduction to the 4d cube and 4d sphere entering our universe
Visualizing 4D Hypercube By Mapping onto a 3D Tesseract (Alan B Scrivener)
Visualizing the Hypercube (Zbigniew Fiedorowicz)

Time as a dimension
The Four Dimension: A Brief Introduction (James Richard Skemp)
Is "Time" Really the Fourth Dimension? (David McNaughton)
Time, the Fourth Dimension (Jim Loy)

Two dimensions
Adventures in Flatland - about a 15 minute stop-action movie the authors made.
Yendred's homepage - hero of the Planiverse.

In-depth discussion of the fourth dimension
Four-Dimensional Geometry (MathWorld)
4th dimension: Selected Course Notes (Davide P. Cervone) - course notes from Math 53, a course on visualizing the fourth dimension, at Union College
Fourth Dimension (Uncle Taz) - several articles from other sources discussing aspects of the fourth dimension
Fourth Dimension (G4G4) - several articles about things like the relation between Fermat's Last Theorem and the fourth dimension, 4-dimensional packing, and four dimensional knots
Fourth Dimension in Modernist Art and Literature (Brad Ricca)
Hypercube's Homepage (Eric Saltsman, aka Hypercube) - philosophy, math, and cosmology related to the fourth dimension.
Hyper Dimensia (Don V Black) - mathematical, scientific, technological, and philosophical implications of higher dimensions
Math Awareness Month 2000: Essays on Dimensions (MathAware.org) - published essays on the dimensions
Miscellaneous Mathematical Musings (Bill Price) - introduction to dimensions, multi-dimensional geometric units, and formulas for calculating higher-dimensional phenomena
Thinking 4-D (Jeff Fuquay) - focuses on helping the reader to conceive of the fourth spatial dimension, discusses hypercubes and hyperspheres

Technical papers
Arbitrary-Dimensional Solid Object Display Algorithm (Greg Ferrar) - algorithm for displaying objects in arbitrary dimensions.
Four-Space Visualization of 4D objects (Steve Hollasch) - mathematical and computer programming oriented approach, discussing wireframe rendering and ray-tracing
4-dimensional optics, gravitation and quantum mechanics (Jose Borges de Almeida) - a theory of optics with dimensions 1-3 being the physical dimension, and dimension 0 being related to its speed

Geometry
Four dimensional figures page (George Olshevsky, aka Polycell) - tabulates all of the convex uniform polychora (four-dimensional polytopes)
A 4-dimensional sphere, animated (Harry Foundalis) - discussion of the mathematics of a 4-dimensional sphere, and what it looks like
The Fourth Dimension (John Savard) - description of four dimensional polytopes, with images
Gallery of Mathematics / Hyperspace Structures (Andy Burbanks and Keith Beardmore) - information about a couple higher dimensional shapes.
n-dimensional.de (Hans Niedermann) - some images of hypercubes and Sierpinski triangles, with the java source code to generate them
Student of Hyperspace (Eric Swab) - computer projections of the six regular polyhedra that exist in 4-space
Uniform Polychora (Jonathan Bowers, aka Hedrondude) - uniform polychora and the short names he has given them, plus POVray rendered three-dimensional cross sections of them
4D Euclidean space (quickfur) - information on visualization, plus pictures and descriptions of 4D uniform polychora and rotopes
The Polygloss (Wendy Krieger) - a glossary of polytope-related terms

Dimensions in modern physics
Extra Dimensions (John Terning) - Introduction to kaluza klein theories and large and warped extra dimensions, plus author's current research on extra dimensional theories
Hyperspheres, Hyperspace, and the Fourth Spatial Dimension (Michael Feltz) - discussion on the fourth spatial dimension and its relation to the curvature of space
In Search of Extra Dimensions (SpaceDaily) - article about the search for extra dimensions in modern physics
Looking for Extra Dimensions (Patricia Schwarz) - introduction to dimensions and string theory, braneworlds, and supersymmetry
Origin and Evolution of the Universe: Extra Dimensions (Michael B Williams) - introduction to extra dimensions in physics, and their relation to the effort to unify quantum mechanics and general relativity
The Search for Extra Dimensions (PhysicsWeb) - article about branes, unification of forces, and gravitons
Theories with Extra Dimensions (Phenomology Institute) - introduction to dimensions being used to unify the forces

Java Applets
4D Model: Tesseract (Harry J Smith) - a rotatable tesseract
4-D Polytope viewer (Michael Gibbs) - a polytope viewer that shows fifteen different polytopes, and also a Draw4d dos program that displays polytopes
4th Dimension (Mark Sudduth) - LiveGraphics3d applets that show three- and four-dimensional surfaces like the klein bottle, pseudo-spheres, and figure-8 torus, with explanations of what the shapes are
Flatland: Triangle (Nicholas Jackiw) - Java Sketchpad applet that gives you a flatlander view as you move a flatlander and a triangle around in a small 2d world
Four dimensional maze - navigate the maze by moving among multiple square mazes
Hypercube by Harmen (Harmen van der Wal) - short introduction to the fourth dimension, plus a hypercube java applet game
Hyperspace Simulation with arbitrary number of dimensions (Domenico De Riso) - applet showing the intersection of an n-dimensional hypercube with a plane of n-1 dimensions
Java Examples (Richard Koch) - displays all the regular three and four dimensional solids, rotatable through buttons
Regular 4d Polytope foldouts
Rotating Four-Dimensional Shapes (Mark E. Shoulson) - hypercube and simplex, which can be rotated by clicking buttons
Seeing into four dimensions (Ken Perlin) - a mouse-rotatable hypercube, hyper-simplex, 4d knots, klein bottle, and other shapes. The applet has an open API, so you can define javascript calls in your own webpage to display your own shapes with the applet
Stereoscopic Animated Hypercube, 24-Cell Object, Cross-Polytope, Simplex Object (Mark Newbold) - stereoscopic rotating shapes, which pop out at you if you have 3d glasses. Also by Mark Newbold: Hyperspace Start Polytope Slicer, Mark Newbold's Rhombic Dodecahedron Page, and HyperSpace Polytope Slicer
The Tesseract (2) (Alex Bogomolny) - allows you to rotate the tesseract around one plane at a time

Programs, multimedia
f00Dave's Tesseract Viewer Demo - opengl demo that displays a tesseract.
Hyper (Mike D'Zmura) - explorable 4d environment that is controlled similar to a first person shooter.
Knotted Spheres in the Fourth Dimension (Andrew J Hanson) - A small mpg of a "knotted-sphere" (a knotted two-manifold embedded in 4d space).
nklein software (Patrick Stein) - non-orientable software in any dimension: ray-tracer for multi-dimensional images.
Polytope visualization: Peek (Gordon Kindlmann) - program for displaying projections and cross sections of n-dimensional polytopes.
Russell Towle's 4D Star Polytope Animations (Russell Towle) - Quicktime animations of four-dimensional star polytopes.
James Lawrence - created Hyperman, a four-dimensional viewer

Games
4D Maze Game (John McIntosh) - four dimensional maze game to download.
4-dimensional crossword (Chris Benn) - 4-dimensional crossword puzzle that was originally published 1989 in Gemini.
Magic cube 4d (Don Hatch and Melinda Green) - four dimensional rubik's cube

Books
Flatland (2 3 4 5) - the complete text of Edward Abbott Abbott's classic book.
Flatland (Joshua Bell) - reviews of books about dimensional subjects.
Fourth dimension writings - Charles Hinton's fourth dimensional writings
Hyperspace in Science Fiction (Sten Odenwald) - a review of the use of hyperspace in science fiction.

Authors
Thomas Banchoff - wrote "Beyond the Third Dimension"
Rudy Rucker - wrote "The Fourth Dimension"
Clifford Pickover - wrote "Surfing Through Hyperspace"
A.K. Dewdney - wrote "Planiverse"

Link lists
Rob Kusner - professor that focuses on "variational problems in low dimensional geometry and topology".
Math 100, Calvin College (Randall Pruim) - Elements of Modern Mathematics (Spring 2003). Some links to fourth dimension webpages.
The 4D Web Page (Mike D'Zmura) - links to sites about different aspects of the fourth dimension: people, books, sites, software, etc.
4 dimensional visualization resources on the WWW - links to 4d visualization sites
Articles VR and 4d - many broken links
The Geometry Junkyard: Many-dimensional Geometry - a lot of links to multi-dimensional sites
Psyche's Links - links to pages on dimensional subjects.

[quickfur]

This page hasn't been updated for 3 years or more. Many of these links are dead, sad to say.

Under "short introductions", the following are dead:

Bogglers: Hyperspace: Up, Out, and Away (Discover Magazine)
Dimensions (The Tesseract School) - hypercubes up to the seventh dimension
Dimensionality (Dwight Vincent) - a discussion involving the history of dimensionality
E. Mayev's Fourth Dimension (Emil Mayev)
Higher Dimensions (Lee Stemkoski)
Hypercubes (Jonathan Bowen) - introduction to n-dimensional objects
An Introduction to the Fourth Dimension and Beyond (Gerald Clement St. Germane)
On the Fourth Dimension (James McManus)
Topology and Juggling: Four-Dimensional Braids (Brown University)
Understanding Dimensions (Vivek Panda)
What is the Fourth Dimension? (Rick Duval)
Why Bother with Extra Dimensions? (Sanjeev Seahra)


That leaves less than a handful of links that are still working.
In the next section (Visualization):

Visualizing 4 dimensional objects in 3 dimensional space (Gurudev) --- still working, but has become a redirect. Link should be updated.


Under "Time as a dimension":

The Four Dimension: A Brief Introduction (James Richard Skemp)


Under "Two dimensions":

Adventures in Flatland


Under "In-depth discussion of the fourth dimension":

Fourth Dimension (Uncle Taz)
Hypercube's Homepage (Eric Saltsman, aka Hypercube)
Miscellaneous Mathematical Musings (Bill Price)
Thinking 4-D (Jeff Fuquay)


Under "Technical Papers":

Four-Space Visualization of 4D objects (Steve Hollasch) - this link is dead but if you google for Steve Hollasch you'll find a new link to his paper
4-dimensional optics, gravitation and quantum mechanics (Jose Borges de Almeida) - link has moved, needs update


Under "Geometry":

Four dimensional figures page (George Olshevsky, aka Polycell) - Olshevsky's site is dead. Fortunately, it has been archived in archive.org: http://web.archive.org/web/200702040750 ... iform.html
A 4-dimensional sphere, animated (Harry Foundalis) - link moved, needs update
The Fourth Dimension (John Savard)
n-dimensional.de (Hans Niedermann)
Student of Hyperspace (Eric Swab)
Uniform Polychora (Jonathan Bowers, aka Hedrondude) - site has moved, look under: http://www.polytope.net/hedrondude/home.htm


Under "Dimensions in modern physics":

Hyperspheres, Hyperspace, and the Fourth Spatial Dimension (Michael Feltz)
Origin and Evolution of the Universe: Extra Dimensions (Michael B Williams)
Theories with Extra Dimensions (Phenomology Institute)


Under "Java Applets":

4D Model: Tesseract (Harry J Smith)
4-D Polytope viewer (Michael Gibbs)
4th Dimension (Mark Sudduth)
Hypercube by Harmen (Harmen van der Wal)
Hyperspace Simulation with arbitrary number of dimensions (Domenico De Riso)


Under "Programs, Multimedia":

f00Dave's Tesseract Viewer Demo
Hyper (Mike D'Zmura)
Knotted Spheres in the Fourth Dimension (Andrew J Hanson)

Under "Books":

Fourth dimension writings - Charles Hinton's fourth dimensional writings


Whew! This list is much longer than I expected. :-( Good luck wading through it.

[wendy]

My web site (polygloss) has moved: it's now http://www.os2fan2.com/gloss/index.html ,

One might look at 'time as a fourth dimension' in http://www.os2fan2.com/gloss/pghtime.html