Explanation Given Information: D 5 (Symmetries of a regular pentagon). Concept Used: List all the ten elements of D 5 D 5 has order 10 5 reflections 5 − 1 rotations and 1 identity Calculation: There are 5 reflections across lines from vertices to midpoints of opposite sides. From the figure, we can see each vertex together with the adjacent line represents a reflection. There are 5 rotations: 0, 72, 144, 216 and 288

9th Edition

ISBN: 9781305657960

Author: Joseph Gallian

Publisher: Cengage Learning

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Question

Chapter 1, Problem 4E

To determine

To describe in pictures or words the elements of D5 .

Expert Solution & Answer

Chapter 1 Solutions

Contemporary Abstract Algebra

Ch. 1 - Prob. 1E Ch. 1 - Prob. 2E Ch. 1 - In D4 , find all elements X such that a. X3=V ; b....Ch. 1 - Prob. 4E Ch. 1 - For n3 , describe the elements of Dn . (Hint: You...Ch. 1 - In Dn , explain geometrically why a reflection...Ch. 1 - Prob. 7E Ch. 1 - Prob. 8E Ch. 1 - Associate the number 1 with a rotation and the...Ch. 1 - If r1,r2,andr3 represent rotations from Dn and...

Ch. 1 - Suppose that a, b, and c are elements of a...Ch. 1 - Prob. 12E Ch. 1 - Find elements A, B, and C in D4 such that AB=BC...Ch. 1 - Explain what the following diagram proves about...Ch. 1 - Prob. 15E Ch. 1 - Describe the symmetries of a parallelogram that is...Ch. 1 - Describe the symmetries of a noncircular ellipse....Ch. 1 - Prob. 18E Ch. 1 - Prob. 19E Ch. 1 - Determine the symmetry group of the outer shell of...Ch. 1 - Let X,Y,R90 be elements of D4 with YR90andX2Y=R90...Ch. 1 - If F is a reflection in the dihedral group Dn find...Ch. 1 - What symmetry property do the words “mow,” “sis,”...Ch. 1 - For each design below, determine the symmetry...Ch. 1 - What group theoretic property do uppercase letters...

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Similar questions

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