3D and 4D tutorial pages written by Paideia students

These are tutorial materials for the Four Dimensions short term class at The Paideia School.

Document description document type document

Duality and 3D Tutorial, containing work by Thomas Leavett '00 and Andrew Berry '00. This is a good place to start.

pdf Duality and 3D tutorial.pdf

Justin Baker's ('00) intro to 4 dimensions, written as a handout to my 4D class each year. Justin is as interested in the mechanism of perception as the math, so this document discusses how we see 3D and how we might see 4D as well as how to draw and understand mathematical objects.

pdf justin 4d.pdf

Descriptive Topology -- Justin Baker's ('00) drawing tutorial.

web pages justin drawing

4D sketchpad -- if we get this together this page links to the spectacular work done here on 4D using Sketchpad.

link not implemented

Misc 3D and 4D pictures -- web pages showing a gallery of 3D and 4D work by Paideia students.

web pages pictures

speculations about the hypersphere by a current student.

web pages not yet

Michael Matthew's ('96) Reflections on Duality. This was written for Thomas Banchoff's 4D class at Brown University. This is really good because, as he writes, we can see Michael begin to understand and we share his understanding.

pdf Unfolding duality.pdf

Michael Matthew's ('96) Beyond 3D. .This is a description of 3D and the stereographic projection, leading up to 4D rotations and the Clifford Torus. Recommended.

pdf beyond 3D.pdf

Our 120 cell adventure

web pages