| Class Schedule |
- A
Half-turn is the product of two line reflections -- in perpendicular
lines.
- A glide reflection, being defined as the product of a translation
and a line reflection, is the product of 3 line reflections, two of
the lines being perpendicular to the invariant line.
- Grouping together with associativity, the glide reflection is actually
the product of a half-turn and a line reflection. The invariant line
of the glide reflection passes through the center of the half turn and
is perpendicular to the mirror line of the line reflection.
- Proof of the nature of triple line reflections (problems 17-19, proving
the missing part of Theorem 12).
- To compose a line reflection, with a general rotation, write the
rotation as the product of two line reflections, one of them chosen
to be perpendicular to the mirror line.
- The case of the product of 3 mirror lines is generally the product
of a line reflection and a rotation, as above. (With some special
cases for parallel lines.)
- Semi-quiz B - on basics of behavior
of isometries
Links to class overheads and notes
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