Geometry

Archimedes' Book of Lemmas
A collection of all 15 propositions from Archimedes' Book of Lemmas with complete proofs, each accompanied by a Java illustration.
http://www.cut-the-knot.org/Curriculum/Geometry/BookOfLemmas/index.shtml

Bette Veteto's Homepage
History of Mathematics, very strong on geometry.
http://www.people.memphis.edu/~brveteto/

Bob's Pages
A collection of interactive geometry applets. Topics include polyhedra, Poncelet's porism, Soddy's hexlet, Mandelbrot set, Steiner porism, Pappus's chain, Repulsion polyhedra and stereo pictures.
http://members.ozemail.com.au/~llan/

Center of Points in 2- or Higher-dimensional Space
It provides important formulations for finding a center of points in 2 or higher dimensional space. It can be used in drawing delauney triagulation and voronoi diagram in two or higher dimensions. It also describes how many points are required in defining a center in n-dimensional space.
http://www.geocities.com/kiranisingh/center.html

The Complete Quadrilateral
Several properties of the complete quadrilateral illustrated with Java applets
http://www.cut-the-knot.org/ctk/CompleteQuadrilateral.shtml

Conjectures Produced by the Program Graffiti
Graffiti is a computer program that makes conjectures in mathematics and chemistry. Links to the conjectures and bibliography.
http://cms.dt.uh.edu/faculty/delavinae/research/wowref.htm

Cuboid and Cube Surface Distances
A java applet with substantial analysis related to distances on a rectangular box.
http://www.btinternet.com/~se16/js/cuboid.htm

Cut the Knot
Features articles about specific problems, illusions, and puzzles. Includes diagrams.
http://www.cut-the-knot.org/geometry.shtml

Encyclopedia of Triangle Centers
By Clark Kimberling. Over 1000 triangle centres in a searchable compilation with diagrams.
http://faculty.evansville.edu/ck6/encyclopedia/

The Entropy Reduction Laboratory by Karl-Dietrich Neubert
Discusses double shell structured periodic systems, platonic spheres, molecular and crystal structures, and FlashSort algorithms.
http://www.neubert.net/

Erich's Packing Center
Graphics and links for various packing, tiling and covering problems.
http://www.stetson.edu/~efriedma/packing.html

Fundamentals of Geometry
Free online book on geometry in pdf format. Contains material not easily found elsewhere from detailed exposition of elementary absolute geometry based on Hilbert's axioms to more advanced topics.
http://polly.phys.msu.ru/~belyaev/geometry.htm

A Gallery of Interactive On-Line Geometry
At the Geometry Center.
http://www.geom.uiuc.edu/apps/gallery.html

Geometric Group Theory
Information and resources about geometric group theory and low-dimensional topology. People, groups, meetings, links.
http://www.math.ucsb.edu/~jon.mccammond/geogrouptheory/

Geometry Activities
By Ephraim Fithian.
http://homepage.mac.com/efithian/geometry.html

Geometry and the Imagination in Minneapolis
Geometry exercises for a two-week summer workshop led by John Conway, Peter Doyle, Jane Gilman and Bill Thurston at the Geometry Center in Minneapolis, June 1991.
http://www.geom.uiuc.edu/docs/doyle/mpls/handouts/handouts.html

Geometry Center
Web site for the (now closed) Center for the Computation and Visualization of Geometric Structures at the University of Minnesota. Graphics, multimedia, software, teaching resources.
http://www.geom.uiuc.edu/

Geometry Formulas and Facts
Excerpts from the 30th Edition of the CRC Standard Mathematical Tables and Formulas (1995), namely, the geometry section minus differential geometry.
http://www.geom.uiuc.edu/docs/reference/CRC-formulas/

Geometry from the Land of the Incas
Presents problems involving circles and triangles, with proofs, SAT practice quizzes and famous quotes. Also, has examples of geometry in Peruvian culture.
http://agutie.homestead.com/

Geometry in Action
Includes collections from various areas in which ideas from discrete and computational geometry meet real world applications.
http://www.ics.uci.edu/~eppstein/geom.html

The Geometry Junkyard
Usenet clippings, web pointers, lecture notes, research excerpts, papers, abstracts, programs, problems, and other stuff related to discrete and computational geometry.
http://www.ics.uci.edu/~eppstein/junkyard/

Geometry Page from Interactive Mathematics Miscellany
Includes articles on topics in elementary and not so elementary geometry, many with interactive Java illustrations and multiple proofs.
http://www.cut-the-knot.com/geometry.html

Geometry/Topology at Michigan State University
Activities of the geometry/topology group at Michigan State University.
http://www.math.msu.edu/gt/

GLaD Comments
A new type of geometric construction that was discovered by Dan Litchfield and David Goldenheim. Includes general explanation and sketch examples.
http://jwilson.coe.uga.edu/Texts.Folder/GLaD/GLaD.Comments.html

Go Geometry
Offers a variety of resources for teaching and learning about geometry. Problems and theorems are presented with step-by-step solutions for each proof.
http://www.gogeometry.com

The Kepler Conjecture
Information on the recent proof of Kepler conjecture on sphere packings.
http://www.math.pitt.edu/~thales/kepler98/

The Lepidoptera of the Circles
The Butterfly theorem and its generalizations illustrated by Java applets.
http://www.cut-the-knot.org/ctk/Lepidoptera.shtml

Math 3210 - Higher Geometry I
Course notes by Bill Cherowitzo.
http://www-math.cudenver.edu/~wcherowi/courses/m3210/m3210.html

Math Forum: Geometry POW/POM Search
Search the Geometry Problem of the Week's archive of creative, non-routine challenges, as well as submissions and commentary, dating back to 1993.
http://mathforum.org/powgrepform.html

Math Forum: Geometry.research
Discussion board for geometry professors and instructors to keep informed of the latest research.
http://mathforum.org/kb/forum.jspa?forumID=130

Math Forum: Search geometry-forum
Those interested in examining the previous incarnation of the Math Forum may search the archives of the Geometry Forum.
http://mathforum.org/kb/forum.jspa?forumID=126

Mathematical Curves and Surfaces
Graphical representations of computer generated forms. (French/English).
http://pagesperso-orange.fr/roger.assouly/

Morley's Miracle
A discussion of Morley's famous theorem and the research of which it was a tiny part. 5 proofs are given including J. Conway's, D. Newman's, and A. Connes'.
http://www.cut-the-knot.com/triangle/Morley/index.html

New Mathematical Findings by Secondary Students
High school students solve complex geometric problems by using GLad Sketchpad. Page includes diagrams.
http://www.javeriana.edu.co/universitas_scientiarum/universitas_docs/vol6n2/ART1.htm

Packomania
Includes packings of equal objects in containers together with source codes to obtain them numerically.
http://hydra.nat.uni-magdeburg.de/packing/packing.html

Paul Bourke's Geometry Page
Includes formulas, definitions and three dimensional image illustrations.
http://astronomy.swin.edu.au/~pbourke/geometry/

Polyedergarten
Shows paper models of polyhedra.
http://www.polyedergarten.de

Problem of the Minimum Rotation Surface
Java applet demonstrating the catenary.
http://home.imm.uran.ru/iagsoft/PMRS_J.html

Sangaku: Reflections on the Phenomenon
Critical reflections on the sangaku phenomenon accompanied by a collection of solved sangaku problems, many with interactive Java illustrations.
http://www.cut-the-knot.org/pythagoras/Sangaku.shtml

Steiner Surfaces
Mathematical descriptions and ray-traced images of various types of Steiner surfaces.
http://www.ipfw.edu/math/Coffman/steinersurface.html

Tim Lister's Hyperbolic Geometry
Cabri constructions for the demonstration of the basic concepts of hyperbolic geometry in the Poincare disc model.
http://mcs.open.ac.uk/tcl2/nonE/nonE.html

Wilson Stothers' Inversive Geometry and CabriJava Pages
Includes Steiner's Porism and the arbelos.
http://www.maths.gla.ac.uk/~wilson/cabripages/inversive/inversive0.html

Xah's Personal Page
Features an illustrated dictionary of special plane curves, a paper on wallpaper groups, mathematics image gallery and links to software packages.
http://xahlee.org/PageTwo_dir/more.html

NPR : Mathematicians Get Crafty with Geometry
A husband and wife from Cornell University have come up with a crafty way to illustrate high-level geometry concepts -- by manipulating yarn into models that help explain the curvature of spaces. The mathemeticians talk with NPR's Jacki Lyden about hyperbolic crocheting. [4:47 streaming audio broadcast] <small>(March 13, 2005)</small>
http://www.npr.org/templates/story/story.php?storyId=4531695