Ring a gap between two circles with smaller circles — does the chain always close?
Draw one large circle and a smaller circle fully inside it, off-centre. Now try fitting a chain of even smaller circles into the ring-shaped gap between them, each one touching its two neighbours and both original circles, all the way around until the chain closes back on itself. Does it matter where you place the very first small circle?
Reveal the answer
No — Steiner's porism says that whether the chain closes perfectly depends only on the two original circles, not on where the first small circle is placed: if it closes for one starting position, it closes for every starting position, always using the same number of circles. Swiss mathematician Jakob Steiner proved this in the 19th century using a transformation that turns the two unequal circles into two concentric ones, where the pattern becomes obvious.