Search IntMath
Close

# Rotational Symmetry in Geometry

In geometry, rotational symmetry is a form of symmetry that occurs when an object can be rotated about a fixed point without changing its overall appearance. A classic example of rotational symmetry is a snowflake, which has sixfold rotational symmetry (meaning it can be rotated by 1/6th of a turn and still look the same).

## How Rotational Symmetry Works

To understand rotational symmetry, let's first consider regular polygons. A regular polygon is a closed figure with sides that are all the same length and angles that are all the same size. Regular polygons always have at least three sides, but there is no upper limit to how many sides they can have.

All regular polygons have rotational symmetry. For example, a triangle has threefold rotational symmetry because it can be rotated by 1/3rd of a turn (120°) and still look the same. Likewise, a square has fourfold rotational symmetry because it can be rotated by 1/4th of a turn (90°) and still look the same. The number of times that a regular polygon can be rotated and still look the same is equal to the number of sides it has.

Not all figures have rotational symmetry. For example, an irregular polygon is a closed figure with sides that are not all the same length or angles that are not all the same size. Irregular polygons do not have any rotational symmetry because they cannot be rotated about a fixed point without changing their overall appearance.

## Conclusion:

Rotational symmetry is a type of symmetry that occurs when an object can be rotated about a fixed point without changing its overall appearance. All regular polygons have rotational symmetry; the number of times that a regular polygon can be rotated and still look the same is equal to the number of sides it has. Not all figures have rotational symmetry; irregular polygons do not have any rotational symmetry because they cannot be rotated about a fixed point without changing their overall appearance.

## FAQ

### What is hypotenuse in simple words?

The hypotenuse is the longest side in a right angled triangle. It is opposite the angle of 90 degrees (the right angle).

### How do you find the hypotenuse?

The length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

### What is an example of a figure with no rotational symmetry?

An irregular polygon is a closed figure with sides that are not all the same length or angles that are not all the same size. Irregular polygons do not have any rotational symmetry because they cannot be rotated about a fixed point without changing their overall appearance.