Order of Rotational Symmetry

Definition of Order of Rotational Symmetry:

The number of times a figure fits into itself in one complete rotation is called the order of rotational symmetry.

If A° is the smallest angle by which a figure is rotated so that rotated from fits onto the original form, then the order of rotational symmetry is given by \(\frac{360°}{A°}\), [A° < 180°]

Order of rotational symmetry = \(\frac{360}{\textrm{Angle of Rotation}}\)

A figure has a rotational symmetry of order 1, if it can come to its original position after full rotation or 360°.

Examples of Order of Rotational Symmetry:

Rectangle (clockwise)

Order of Rotation

We observe that while rotating the figure through 360°, it attains original from two times i.e., it looks exactly the same at two positions. Thus, we say that the rectangle has a rotational symmetry of order 2.

Equilateral triangle (clockwise):

Order of Rotational Symmetry

We observe that at all 3 positions, the triangle looks exactly the same when rotated about its center by 120°.


Letter B (clockwise):

Definition of Order of Rotational Symmetry

We observe that only at one position the letter looks exactly the same after taking one complete rotation.


Windmill (anticlockwise):

anticlockwise

We observe that if we rotate it by one – quarter, at 4 positions, it looks exactly the same. Therefore, the order of rotational symmetry is 4.



Solved Examples on Order of Rotational Symmetry:

1. Find the order of rotational symmetry of the following shapes about the point marked.

Problems on Rotational Symmetry

Solution:

(i)

Problems on Order of Rotational Symmetry

Order of rotational symmetry = \(\frac{360}{180}\) = 2


(ii)

Rotational Symmetry Problems

Order of rotational symmetry = \(\frac{360}{60}\) = 6


2. The figure obtained by giving 2 anticlockwise right-angle turns to letter G is:

2 Anticlockwise Right-angle Turns

Answer: (ii)



● Related Concepts

Linear Symmetry

Lines of Symmetry

Point Symmetry

Rotational Symmetry

Types of Symmetry

Reflection

Reflection of a Point in x-axis

Reflection of a Point in y-axis

Reflection of a point in origin

Rotation

90 Degree Clockwise Rotation

90 Degree Anticlockwise Rotation

180 Degree Rotation










7th Grade Math Problems

8th Grade Math Practice

From Definition of Order of Rotational Symmetry to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Share this page: What’s this?

Recent Articles

  1. Types of Fractions |Proper Fraction |Improper Fraction |Mixed Fraction

    Jul 12, 24 03:08 PM

    Fractions
    The three types of fractions are : Proper fraction, Improper fraction, Mixed fraction, Proper fraction: Fractions whose numerators are less than the denominators are called proper fractions. (Numerato…

    Read More

  2. Worksheet on Fractions | Questions on Fractions | Representation | Ans

    Jul 12, 24 02:11 PM

    Worksheet on Fractions
    In worksheet on fractions, all grade students can practice the questions on fractions on a whole number and also on representation of a fraction. This exercise sheet on fractions can be practiced

    Read More

  3. Fraction in Lowest Terms |Reducing Fractions|Fraction in Simplest Form

    Jul 12, 24 03:21 AM

    Fraction 8/16
    There are two methods to reduce a given fraction to its simplest form, viz., H.C.F. Method and Prime Factorization Method. If numerator and denominator of a fraction have no common factor other than 1…

    Read More

  4. Conversion of Improper Fractions into Mixed Fractions |Solved Examples

    Jul 12, 24 12:59 AM

    To convert an improper fraction into a mixed number, divide the numerator of the given improper fraction by its denominator. The quotient will represent the whole number and the remainder so obtained…

    Read More

  5. Conversion of Mixed Fractions into Improper Fractions |Solved Examples

    Jul 12, 24 12:30 AM

    Conversion of Mixed Fractions into Improper Fractions
    To convert a mixed number into an improper fraction, we multiply the whole number by the denominator of the proper fraction and then to the product add the numerator of the fraction to get the numerat…

    Read More