Number PatternsCircumference & AreaEasy
The π Illusion
A glass's rim is far longer around than the glass looks tall — π makes sure of it.
Worked demonstration
A glass has a rim 15 cm across (its diameter). Using the rule circumference = π × diameter, how far is it around the rim, to the nearest centimetre?
Try it yourself
Why it works
Circumference = π × diameter ≈ 3.14 × diameter, so the way around a rim always beats its apparent height by about three times.
Background & Explore Further
π and this circumference-vs-height surprise reappear in packaging design and the horizontal-vertical illusion in perception research. Explore how π connects a circle's edge to its width.
Maths Made Magic — Queen Mary University of London (cs4fn)