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