## Tentative Reading Assignments (Revised 6-9-98)

 Assnm't Source Chapter and pages Comments and other things 1 Flatland    Devlin Introduction, Preface, and Part I.  Prologue, pp. 1-7.  Chapter 1, Greek Mathematics, pp. 14 - 18, 21, and 31. (Activity and assignments on Flatland will follow next week.) 2 Flatland  Pedoe Part II.  Preface and Chapter 1 (in part), Vitruvius, pp. 11-31. Bring two congruent equilateral triangles to next class. 3 Devlin  Pedoe pp. 144-150 (Symmetry Groups); pp. 165-169 (Tiling).  pp. 258 (middle) - 261 (symmetry). Symmetry Day: Bring to class an example of a natural or synthetic physical object that has a non- trivial group of symmetries together with your description of those symmetries. You may bring either the physical object itself or a sketch of the object. 4 Devlin    Pedoe pp. 153-157 (lattices and sphere packing);  pp. 163-164 (wallpaper patterns)  pp. 44-46 middle; 66-69 middle. (regular polygons) Tessellation Day: Wear to class clothing that has a tiling pattern on it. 5 Devlin  Pedoe  Barr  Plato pp. 112-115  pp.165-170; pp. 261-263  pp. 1-10  The metaphor of the cave. (Euclid-inscribed angles in semicircles, Platonic solids, Plato, and Kepler)  (tiling) (Platonic solids)  (Introduction to Topology)  (On Handout.) 6 Devlin  Pedoe  Barr pp. 174 - 175; 176 - 178  pp. 265 - 267  pp. 10 - 23 (Topology, Networks, and Euler's formula)  (Semi-regular solids)  (Euler's formula, the torus) 7 Devlin  Barr  Pedoe pp. 188-189  pp. 117-119,120 (first column only)  pp. 23-31  pp.108-119; pp. 173-177 pp. 273-284 (The Four Color Problem)  (Cartesian coordinates) ( The Moebius strip, orientability, and dimension.)  (Map Coloring.)  (Cartesian coordinates) Flatland; the Fourth dimension introduced. 8 Devlin  Barr Pedoe pp. 138-141  pp. 31-39  pp. 273-284 Dimension New Surfaces- the Klein Bottle Flatland; the Fourth dimension introduced.(repreated) 9 Devlin  Barr pp. 179-182; pp. 182-186, 187(1st paragraph.)  pp. 62 - 72 pp. 78 - 84 (The Moebius strip, orientability) (Surfaces)  More about the Klein Bottle Intro to Cross Caps and the Projective Plane 10 Devlin  Barr p. 7. Box...  p.193-197 1st column.  pp. 136-148 (When to See Is to Understand)  ( A side trip to look at knots-a beginning only)  (Turning a punctured torus inside - out) 11 Devlin  Pedoe  Barr  A&S pp. 74-79   pp. 82-85  pp. 102-107  pp. 44 - 58  (Optional)pp. 149-161  pp 1-3 (Zeno's Paradoxes and the infinite.)   The Infinite Scale and proportion Durer and perspective drawing (Continuity and Discreteness)  (Beginning to discuss configurations) 12 Devlin  Pedoe  A&S p. 129 - 133  pp. 44 - 58  Sections 3 and 6. (Projective Geometry)  (Durer and perspective drawing)  (Projection and Ideal elements) 13 Devlin  Pedoe  A&S p. 114-115; p. 115-119  p. 134-138  p. 58-65; p. 173-184  Section 11. (Kepler's Planetary Theory) (Conics and cartesian geometry)  (Continuation of Projective geometry)  (Durer, conics and perspective drawing cont'd.) (Cartesian & Projective geometry-Desargue again)  (Desargue's Theorem) 14 Devlin Pedoe pp. 106-109; pp. 122-129  pp.184-192 (Euclid's Axioms) (Non-Euclidean Geometries)  (Drawing & projective geometry)