Day 21

Math 444, Monday, 11/14

Sponsor Today's class is brought to you by Triple Line Reflections
Topics Solving equations of isometries An important theorem that Isometries are all products of line reflections.
Class Schedule
  • Definition and properties of glide reflections
  • Translations and glide reflections are isometries because compositions of isometries are isometries.
  • Solving ab = cd for c or d. Notes with solutions.
  • Given 3 parallel lines m1, m2, m3, denote the reflections in these lines by M1, M2, M3. The triple reflection M3 M2 M1 is a line reflection. Construct the line n so that N, the line reflection in n satisfies N = M3 M2 M1.
  • Fundamental Theorem 11: All isometries are compositions of 1, 2 or 3 line reflections.
  • Fundamental Theorem 12: All isometries are translations, rotations, line reflections or glide reflections (part of proof next time)
Assignments
New

Reading Assignment (due Wednesday 11/16)

Read: Brown, Sections 1.10, 2.1, 2.4

Due Today

Read Brown, 1.7, 1.8

Ongoing

Assignment 8 (due Wed 11/16)

Construction Portfolio 4 (due Monday 11/21)..

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