Describe Types of Symmetry

Discussion in 'Algebra' started by nycmathguy, Jun 8, 2022.

1. nycmathguy

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I see that there is symmetry with respect to x-axis and y-axis. Algebraically, it can be shown that there is symmetry with respect to the origin. How does the graph show symmetry with respect to the origin?

nycmathguy, Jun 8, 2022
2. MathLover1

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When considering all the lines of symmetry in a circle, we simply take all of its diameters which is infinitely many.
A circle is thus said to be symmetric under rotation or to have rotational symmetry.
Symmetry comes in two forms: reflectional and radial.
Reflectional symmetry is symmetry across a line of symmetry; radial symmetry is symmetry about a center point.

A circle (somewhat trivially) has both of these kinds of symmetries. Since a circle has infinitely many diameters, it has infinitely many lines of reflectional symmetry. Furthermore, any size sector in the circle can be rotated about the center point, so this creates infinitely many instances of radial symmetry.

MathLover1, Jun 8, 2022
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3. nycmathguy

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In other words, my reply is incorrect. Yes?

nycmathguy, Jun 8, 2022