Traveller whose Head goes Further than Feet

Problem

 * A traveller sets out on a journey,
 * and eventually returns to the place where he started.
 * During his journey, his head has travelled $12$ yards further than his feet,
 * and yet his head remains attached to his body.
 * How is this possible?

Solution
The traveller went around the world, at the equator.

Proof
Let the radius of Earth at the equator be $R$.

Thus, by Perimeter of Circle, the equator measures $2 \pi R$ all the way round.

Let the height of the traveller be $h$ yards.

Consider the equation:
 * $12 = 2 \pi \paren {R + h} - 2 \pi R$

Thus we have:
 * $h = \dfrac {12} {2 \pi} \approx 1.91$

So, if the traveller:
 * were $1.91$ yards, that is, approximately $5$ feet $9$ inches tall
 * and walked the entire way around the world, along the equator,

his head would have travelled $12$ yards further than his feet.