Rotational symmetry occurs when an object can be rotated around a central point and still look the same. The Rotational Symmetry Calculator is a tool designed to help you understand and apply this concept efficiently. By inputting the characteristics of a shape, it calculates the order of rotational symmetry, making it easier to visualize and comprehend how a shape can be rotated to mirror its original position.

## Formula of Rotational Symmetry Calculator

To find the order of rotational symmetry, you need to:

- Identify the center of rotation of the shape.
- Look for lines of symmetry or examine how many full rotations it takes for the shape to appear identical to itself.
- Divide 360 degrees by the number of rotations needed (number of lines of symmetry for some shapes).

This calculation gives you the order of rotational symmetry in degrees. For instance, a square has 4 lines of symmetry. Therefore, following the formula: 360∘/4=90∘. This means a square has rotational symmetry every 90∘.

## Table of Common Rotational Symmetries

For your convenience, here's a table listing common shapes and their rotational symmetries. This table serves as a quick reference to understand various shapes' symmetry orders without performing calculations each time.

Shape | Rotational Symmetry Order | Degrees of Rotation |
---|---|---|

Square | 4 | 90° |

Rectangle | 2 | 180° |

Circle | Infinite | 360° |

Equilateral Triangle | 3 | 120° |

Pentagon | 5 | 72° |

This table is a handy guide for quickly identifying the rotational symmetry of common shapes, enhancing your understanding of geometric properties.

## Example of Rotational Symmetry Calculator

Consider an equilateral triangle. It looks the same after being rotate 120∘ each time around its center. This triangle has 3 lines of symmetry, and using our formula, 360∘/3=120∘, it has a rotational symmetry order of 3 or every 120∘.

## Most Common FAQs

**1. What is rotational symmetry?**Rotational symmetry is when a shape can rotate around a central point and still look the same as it did before the rotation.

**2. How do I use the rotational symmetry calculator?**Input the characteristics of the shape into the calculator. It will automatically compute the shape's rotational symmetry order based on the number of times it can rotate and appear unchanged.