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4. Frieze Patterns (wallpaper borders) have patterns that repeat indefinitely in a single direction. It turns out that there are only 7 basic types. They are classified using translations, rotations, reflections, and glide reflections. The classification scheme consists of 2 symbols.

4. Frieze Patterns (wallpaper borders) have patterns that repeat indefinitely in a single direction. It turns out that there are only 7 basic types. They are classified using translations, rotations, reflections, and glide reflections. The classification scheme consists of 2 symbols.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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4. Frieze Patterns (wallpaper borders) have patterns that repeat indefinitely in a single direction. It turns out that there are only 7 basic types. They are classified using translations, rotations, reflections, and glide reflections. The classification scheme consists of 2 symbols. Examples: 11 JJJJJJJJ 1m D D D D D D D D m1 ΑΑΑΑΑΑΑΑ mm X X X X X X X X 12 ZZZZZZZZ 1g p b p b p b p b mg p q b d p q b d Translation only Horizontal line of Reflection (& Glide Reflection) Vertical line of Reflection Both Horizontal & Vertical lines of Reflection, 180° Rotation, (& Glide Reflection) 180° Rotation Glide Reflection Vertical line of Reflection, 180° Rotation, & Glide Reflection Determine the classification code for each of the following: (a) (b) 会会会会 *Σ; ** S+5+5+5 (c) <3<3<3 (d)
Transcribed Image Text:4. Frieze Patterns (wallpaper borders) have patterns that repeat indefinitely in a single direction. It turns out that there are only 7 basic types. They are classified using translations, rotations, reflections, and glide reflections. The classification scheme consists of 2 symbols. Examples: 11 JJJJJJJJ 1m D D D D D D D D m1 ΑΑΑΑΑΑΑΑ mm X X X X X X X X 12 ZZZZZZZZ 1g p b p b p b p b mg p q b d p q b d Translation only Horizontal line of Reflection (& Glide Reflection) Vertical line of Reflection Both Horizontal & Vertical lines of Reflection, 180° Rotation, (& Glide Reflection) 180° Rotation Glide Reflection Vertical line of Reflection, 180° Rotation, & Glide Reflection Determine the classification code for each of the following: (a) (b) 会会会会 *Σ; ** S+5+5+5 (c) <3<3<3 (d)
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