Perimeter, and why relays have staggers

"Why do runners in outer lanes start ahead?" In a 4 × 100 m relay, the outer lanes go round bigger curves on the bends, so they are longer. The head start, called the stagger, makes every lane the same length. It is fair, not a gift.

Perimeter is the total length round a shape's border: the distance a tiny insect walks to get back to where it started, or the length of fence round a park.

Familiar perimeters:

• square of side a: 4a;
• equilateral triangle of side a: 3a;
• rectangle a by b: 2(a + b) (a square is the special case b = a).

Ratios that never change. Double a square's side and its perimeter doubles too: perimeter : side is always 4 : 1. For equilateral triangles it is always 3 : 1.

A circle's perimeter is its circumference. Is circumference : diameter the same for every circle? Yes. Every circle is a scaled copy of every other, so this ratio, the C/D ratio, is one fixed number.

A smaller track does not shrink the stagger. The extra length on a bend depends only on the lane width and on how far the runner turns. A 400 m race on a 200 m track goes round twice, so the stagger is twice as big.