What is Rotational Symmetry?
Contents
Definition: Rotational symmetry is the property a shape has when it looks the same after some rotation (partial turn). In Biology the rotational symmetry is also known as radial symmetry.
The rotational symmetry of a shape explains that when an object is rotated on its own axis with a turn of less than full turn, the shape of the object looks same.
Angle of Rotational Symmetry
Characteristics
If a figure has rotational symmetry the image coincides with the pre-image when it is rotated by an angle between 0° and 360°.
If a figure has rotational symmetry and you rotate it around the center with a partial turn then it will look just as same as it before the rotation.
Uses
- Rotational symmetry is use by the wind’s motion in modern wind farms to turn their symmetric turbines.
- The parts that have rotational symmetry are used by power plants to generate electricity.
- Hydroelectric plants use rotating turbines to generate electricity.
- By the help of rotational symmetry power plants operate smoothly and produce great quantities of power.
Importance
Rotational symmetry is very important, it is essential for many machines. Without rotational symmetry wheels would stop turning, motors would freeze and the world would come to a halt.
Nature uses symmetry to make things beautiful. For Example- Spiderwort flower has rotational symmetry of order 3 and Clematis flower has rotational symmetry of order 8. Rotational symmetry appears in sea stars, jellyfish, and they look beautiful because they have rotational symmetry.
Order of Rotational Symmetry
The order of rotational symmetry of a shape is the number of times you can rotate the shape during a rotation of 360° so that it looks exactly the same as the original shape.
You can find the order of rotational symmetry by calculating the smallest angle you can rotate the shape through so that it looks exactly same.
There is no rotational symmetry of order 1 if a shape only matches once after a full turn (360°), and then there is no really symmetry.
Common orders and the angle in degrees the object rotates are:
- order 2 = 180°
- order 3 = 120°
- order 4 = 90°
- order 5 = 72°
- order 6 = 60°
- order 7 = a little bit more than 51°
- order 8 = 45°
- order 9 = 40°
- order 10 = 36°
Rotational Symmetry Examples – Order 1- 10
Rotational Symmetry Shapes
Order 1 – rotational symmetry trapezium: A trapezium has a rotational symmetry of order 1.
Order 2 – rotational symmetry rectangle: A rectangle has a rotational symmetry of order 2. A rectangle when rotated about its center by half a turn (180°) its looks exactly same like the original rectangle.
Order 3 – rotational symmetry triangle: An equilateral triangle has a rotational symmetry of order 3. An equilateral triangle when rotated about its center by an angle of 180° its looks exactly same like the original equilateral triangle.
Order 4 – rotational symmetry square: A square has a rotational symmetry of order 4. A square when rotated about its center by an angle of 90° its looks exactly same like the original square.
Order 5 – rotational symmetry pentagon: A star has a rotational symmetry of order 5. A star can be rotated five times along its tip by an angle of 72° each time and it looks exactly same like the original star.
Order 6 – rotational symmetry hexagon: A regular hexagon has a rotational symmetry of order 6. A regular hexagon can be rotated six times with an angle of 60° each time and it looks exactly same like the original regular hexagon.
Order 7 – rotational symmetry heptagon: A regular heptagon has a rotational symmetry of order 7. A regular heptagon can be rotated in such a way that it will look the same as the original regular heptagon seven times in 360°.
Order 8 – rotational symmetry octagon: A regular octagon has a rotational symmetry of order 8. A regular hexagon can be rotated eight times with an angle of 45° each time and it looks exactly same like the original regular octagon.
Order 9 – rotational symmetry nonagon: A regular nonagon has a rotational symmetry of order 9. A regular nonagon can be rotated in such a way that it will look the same as the original regular nonagon nine times in 360°.
Order 10 rotational symmetry: A dartboard has a rotational symmetry of order 10. A dartboard can be rotated ten times by an angle of 36° each time and it looks exactly same like the original dartboard.
What is the order of rotational symmetry for a rhombus?
The rotational symmetry of a rhombus is 2 because it appears the same twice through a complete 360° rotation.
Rotational Symmetry in Letters
The letters H, I, N, O, S, X, and Z have rotational symmetry. If H, I, N, S, X, and Z are rotated by 180° about particular axis, they remain same. Letter O has rotational symmetry of infinite order.
Rotational Symmetry vs Reflective Symmetry – What’s the Difference?
Reflective symmetry is when a shape or pattern is reflected in a mirror line/or a line of symmetry. Reflected image will be at the same distance from the line of symmetry and of the same shape and the size.
Rotational symmetry of a shape is a rotation that maps the shape back to itself such that the rotation is greater than 0° but less than 360°.