(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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F892e817a-9b32-4eeb-b8fc-5dd7ffde6479%2Fc40b7d5d-65f7-4fcf-ad6d-a1a1355371e7%2F2ug0659_processed.png&w=3840&q=75)
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F892e817a-9b32-4eeb-b8fc-5dd7ffde6479%2Fc40b7d5d-65f7-4fcf-ad6d-a1a1355371e7%2Fzivlbf9_processed.png&w=3840&q=75)
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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