The rotational symmetry of a square is 4.
Understanding Rotational Symmetry
Rotational symmetry is a type of symmetry where an object looks the same after being rotated by a certain amount around a central point. The order of rotational symmetry is the number of times the object fits exactly onto itself during a full 360-degree rotation. The angle of rotation is the smallest angle through which the object must be rotated to coincide with its original position.
According to the provided information, a square is a quadrilateral with all internal angles measuring 90 degrees. The reference explicitly states that:
- The order of rotational symmetry of a square is 4.
- This is because it fits into itself 4 times in a complete 360° rotation.
- The angle of rotation is 90°.
How a Square Exhibits Rotational Symmetry of Order 4
Imagine rotating a square around its center point. Let's label the corners A, B, C, and D in clockwise order.
- 0° Rotation: The square is in its original position (ABCD). It fits onto itself.
- 90° Rotation (Clockwise): Corner A moves to where B was, B to C, C to D, and D to A. The square now looks the same as the original square. It fits onto itself. This is the smallest angle of rotation.
- 180° Rotation (Clockwise): Corner A moves to where C was, B to D, C to A, and D to B. The square again looks identical to the original. It fits onto itself.
- 270° Rotation (Clockwise): Corner A moves to where D was, B to A, C to B, and D to C. The square once more aligns perfectly with its original position. It fits onto itself.
- 360° Rotation (Clockwise): The square returns to its original 0° position (ABCD). This is a full rotation, and it fits onto itself, completing the cycle.
During a full 360° rotation, the square fits onto its original position at four distinct angles: 0°, 90°, 180°, and 270°. Since it fits onto itself 4 times (excluding the starting position which is usually counted in the order), the order of rotational symmetry is 4. The smallest angle to achieve this fit is 90°.
Summary of Rotations
| Rotation Angle | Does it Fit Onto Itself? |
|---|---|
| 0° | Yes |
| 90° | Yes |
| 180° | Yes |
| 270° | Yes |
| 360° | Yes |
As shown in the table, the square aligns with its initial position 4 times within a 360° turn (at 90°, 180°, 270°, and 360° or 0°), confirming an order of 4.
Understanding the rotational symmetry of shapes like squares is fundamental in geometry and has applications in various fields, from art and design to physics and engineering.
