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(b) Label the square's vertices as A, B,C, D, and write down each symme- try in tableau form. As in Figure 13.3.1, denote each symmetry by a variable (you may use p1, P2, ... for the rotations and 41, 42,... for the reflections). (c) Write the Cayley table for the symmetries of a square. (d) For each symmetry of a square, list its inverse.

(b) Label the square's vertices as A, B,C, D, and write down each symme- try in tableau form. As in Figure 13.3.1, denote each symmetry by a variable (you may use p1, P2, ... for the rotations and 41, 42,... for the reflections). (c) Write the Cayley table for the symmetries of a square. (d) For each symmetry of a square, list its inverse.

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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Please do Part B,C,D and please show step by step and explain

Exercise 13.3.12. (a) Describe all symmetries of a square (For example, "reflection about the vertical axis " describes one symmetry: give similar descriptions of all symmetries of the square. For rotations, use counterclockwise rotations rather than clockwise: it's the mathy way of doing rotations.) (b) Label the square's vertices as A, B,C, D, and write down each symme- try in tableau form. As in Figure 13.3.1, denote each symmetry by a variable (you may use p1, P2, ... for the rotations and 41, P2,... for the reflections). (c) Write the Cayley table for the symmetries of a square. (d) For each symmetry of a square, list its inverse.
Transcribed Image Text:Exercise 13.3.12. (a) Describe all symmetries of a square (For example, "reflection about the vertical axis " describes one symmetry: give similar descriptions of all symmetries of the square. For rotations, use counterclockwise rotations rather than clockwise: it's the mathy way of doing rotations.) (b) Label the square's vertices as A, B,C, D, and write down each symme- try in tableau form. As in Figure 13.3.1, denote each symmetry by a variable (you may use p1, P2, ... for the rotations and 41, P2,... for the reflections). (c) Write the Cayley table for the symmetries of a square. (d) For each symmetry of a square, list its inverse.
identity (А В С' id = А В В А B B (A B C\ Pi = C A rotation в с A A А ВС (C A B) rotation P2 = B В А В С) с в reflection В А C A А ВС C B A reflection 42 = в с B А В В АС reflection H3 = в в A Figure 13.3.1. Symmetries of an Equilateral Triangle
Transcribed Image Text:identity (А В С' id = А В В А B B (A B C\ Pi = C A rotation в с A A А ВС (C A B) rotation P2 = B В А В С) с в reflection В А C A А ВС C B A reflection 42 = в с B А В В АС reflection H3 = в в A Figure 13.3.1. Symmetries of an Equilateral Triangle
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