
Recent Posts
 StiefelWhitney cycles as intersections
 Schläfli – for lush, voluminous polyhedra
 Slightly elevated Teichmuller theory
 Mr Spock complexes (after Aitchison)
 Roots, Schottky semigroups, and Bandt’s Conjecture
 Taut foliations and positive forms
 Explosions – now in glorious 2D!
 Dipoles and Pixie Dust
 Mapping class groups: the next generation
 Groups quasiisometric to planes
 Div, grad, curl and all this
 A tale of two arithmetic lattices
 3manifolds everywhere
 kleinian, a tool for visualizing Kleinian groups
 Kähler manifolds and groups, part 2
 Kähler manifolds and groups, part 1
 Liouville illiouminated
 Scharlemann on Schoenflies
 You can solve the cube – with commutators!
 Chiral subsurface projection, asymmetric metrics and quasimorphisms
 Random groups contain surface subgroups
 wireframe, a tool for drawing surfaces
 Cube complexes, Reidemeister 3, zonohedra and the missing 8th region
 Orthocentricity
 Kenyon’s squarespirals
Blogroll
 0xDE
 Area 777
 Combinatorics and more
 Deep street soul
 Evaluating EDiscovery
 floerhomology
 Gaddeswarup
 Geometric Group Theory
 Godel's lost letter and P=NP
 Images des mathematiques
 Jim Woodring
 Language Log
 Letters of note
 Low dimensional topology
 Math Overflow
 Math/Art Blog
 Mathematics under the microscope
 nCategory Cafe
 Noncommutative geometry
 Paul Krugman
 Persiflage
 Preposterous Universe
 Questionable content
 Quomodocumque
 Real Climate
 Scott McCloud
 Secret blogging seminar
 Sketches of topology
 Tanya Khovanova
 Terry Tao
 Tim Gowers
 Tony Phillips
Books
Software
Recent Comments
Danny Calegari on Schläfli – for lush, vol… melissa on Schläfli – for lush, vol… ranicki on StiefelWhitney cycles as… Danny Calegari on StiefelWhitney cycles as… ranicki on StiefelWhitney cycles as… Categories
 3manifolds (20)
 4manifolds (2)
 Algebraic Geometry (2)
 Algebraic Topology (1)
 Biology (2)
 Commentary (4)
 Complex analysis (11)
 Convex geometry (2)
 Diophantine approximation (1)
 Dynamics (13)
 Ergodic Theory (8)
 Euclidean Geometry (8)
 Foliations (2)
 Geometric structures (6)
 Groups (31)
 Hyperbolic geometry (25)
 Knot theory (1)
 Lie groups (8)
 Number theory (2)
 Overview (2)
 Polyhedra (3)
 Probability (1)
 Projective geometry (2)
 Psychology (3)
 Riemannian geometry (1)
 Rigidity (2)
 Special functions (2)
 Surfaces (20)
 Symplectic geometry (3)
 TQFT (1)
 Uncategorized (5)
 Visualization (10)
Meta
Category Archives: Visualization
Explosions – now in glorious 2D!
Dennis Sullivan tells the story of attending a dynamics seminar at Berkeley in 1971, in which the speaker ended the seminar with the solution of (what Dennis calls) a “thorny problem”: the speaker explained how, if you have N pairs of … Continue reading
kleinian, a tool for visualizing Kleinian groups
It’s been a while since I last blogged; the reason, of course, is that I felt that I couldn’t post anything new before completing my series of posts on Kähler groups; but I wasn’t quite ready to write my last … Continue reading
wireframe, a tool for drawing surfaces
The purpose of this brief blog post is to advertise that I wrote a little piece of software called wireframe which can be used to quickly and easily produce .eps figures of surface for inclusion in papers. The main use is … Continue reading
Random turtles in the hyperbolic plane
My eldest daughter Lisa recently brought home a note from her school from her computer class teacher. Apparently, the 5th grade kids have been learning to program in Logo, in the MicroWorlds programming environment. I have very pleasant memories of … Continue reading
Circle packing – theory and practice
I am spending a few months in Göttingen as a Courant Distinguished Visiting Professor, and talking a bit to Laurent Bartholdi about rational functions — i.e. holomorphic maps from the Riemann sphere to itself. A rational function is determined (up … Continue reading
The HallWitt identity
The purpose of this blog post is to try to give some insight into the “meaning” of the HallWitt identity in group theory. This identity can look quite mysterious in its algebraic form, but there are several ways of describing it geometrically which … Continue reading
Posted in Groups, Lie groups, Surfaces, Visualization
Tagged commutators, gropes, HallWitt identity, visualization
1 Comment
Hyperbolic Geometry (157b) Notes #1
I am Alden, one of Danny’s students. Error/naivete that may (will) be found here is mine. In these posts, I will attempt to give notes from Danny’s class on hyperbolic geometry (157b). This first post covers some models for hyperbolic … Continue reading →