This exercise shows that the group of symmetries of a certain type of geometric figure may depend

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This exercise shows that the group of symmetries of a certain type of geometric figure may depend on the dimension of the space in which we consider the figure to lie.

a. Describe all symmetries of a point in the real line R; that is, describe all isometries of R that leave one point fixed.

b. Describe all symmetries (translations, reflections, etc.) of a point in the plane R².

c. Describe all symmetries of a line segment in R

d. Describe all symmetries of a line segment in R² .

e. Describe some symmetries of a line segment in R³ .

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A First Course In Abstract Algebra

ISBN: 9780201763904

7th Edition

Authors: John Fraleigh

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Question Posted: Dec 30, 2022 05:41 AM

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This exercise shows that the group of symmetries of a certain type of geometric figure may depend

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a The only symmetry of a point in the real line R is the identity transformation which does ...View the full answer

A First Course In Abstract Algebra

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