Grades K–2 · Mathematics
Why does a round cover stay the same width?
A round cover can turn in its frame without finding a narrow side. A painted stripe may point across it, then slantwise, then up and down. The stripe changes direction, but the circle stays the same width.
A circle's edge is the same distance from its middle all the way around. A straight line across the middle reaches from one edge to the opposite edge. That distance is called the diameter. Turning the circle gives another diameter of the same length.
For the cover pictured here, the clear opening underneath is a little narrower. A rim around the opening supports the cover's edge. Turning the cover flat does not make it narrow enough to fit into that opening. There is no special corner that must point the right way.
The stripe turns, while the blue outline does not change size. The dashed circle represents the opening underneath the cover.
Not every cover is round, and real covers also need strong materials and a good supporting frame. This circle reveals one useful idea: a shape can change the direction it faces while keeping an important measurement exactly the same.
About this explanation
These are ideal top views of a circular cover and a smaller circular opening. Other cover shapes exist, and real covers need a suitable frame.
Starting knowledge: Recognize a circle and compare wider with narrower.
Sources
- Wolfram MathWorld — Curve of Constant Width