A wheel has infinite rotational symmetry.
Understanding Rotational Symmetry
Rotational symmetry refers to the ability of a shape or object to look the same after being rotated by a certain angle. The "order" of rotational symmetry indicates how many times an object looks identical during a full 360-degree rotation.
Rotational Symmetry in Wheels
A perfectly circular wheel possesses infinite rotational symmetry. This means it can be rotated by any angle, however small, and it will still appear identical to its original position. This is because every point on the circumference is equidistant from the center, so rotating it maintains its appearance.
Think of it this way:
- Quarter Turn: Rotate the wheel 90 degrees. It looks the same.
- Half Turn: Rotate the wheel 180 degrees. It looks the same.
- Any Angle: Rotate the wheel by 1 degree, 0.5 degrees, or even an infinitesimally small amount, and it will still appear identical.
Real-World Considerations
While theoretically a wheel has infinite rotational symmetry, in reality, factors like valve stems, logos, tire treads, and other markings break this perfect symmetry. However, the underlying principle of rotational symmetry is what allows wheels to function effectively.
