Readings

Seeing:
from Philosophical Investigations by Ludwig Wittgenstein
Shape: Talking about Seeing and Doing by George Stiny
from Finite and Infinite Games by James P. Carse
The Dot by Armin Hofmann, poster by Tony Pritchard
The Snowman by Wallace Stevens
Teaching to See Like a Mathematician by Walter Whiteley
Edward Tufte's website, including the film Teaching to See about Inge Druckrey

Properties:
Shape
  How to Guard an Art Galley by T.S. Michael
  Polygon Triangulation by Subhash Suri
  Is Every Polygonal Region Illuminable From Some Point? by Victor Klee
  Polygonal Rooms Not Illuminable From Every Point by George W. Tokarsky
Position
  Packing Pennies in the Plane by Bill Casselman
  Erich's Packing Center by Erich Friedman
  Geometric Packing Problems by Joe Malkevitch
  Can You Do Better? by Bill Casselman
  Packing Problem on Wikipedia
Size
  Taxi! by Joe Malkevitch
  Taxicab Geometry: An Adventure in Non-Euclidean Geometry 
      by Eugene F. Krause (I have copies)
  Some problems and solutions for square grid-based fire spread simulation 
      by David Caballero
  Explorations into Euclidean and Taxicab Minimum Distances by Hudson Cooke
  see also: taxicabgeometry.net
Connection
  Sperner's Lemma on Cut the Knot
  Sperner's Lemma on Wikipedia
  The Hairy Ball Theorem via Sperner's Lemma by Tyler Jarvis and James Tanton
  Game Theory and Math Economics: A TCS Introduction by Christos Papadimitriou
Dimension
  Learning to Appreciate Dimension by Kenji Ueno
  Geographic Coordinate System by Jim Riesterer
  Coordinate System on Wikipedia
  Curved Space Geometry by Rafi Moor


Definitions:
from Definitions in Mathematics by Zalman Usiskin et al
Words by Alan Lightman
from Proofs and Refutations by Imre Lakatos
Definitions from Euclid's Elements
An Euler diagram of types of triangles
from Creswell's Geometry (1819)