Perimeter - Perception of Perimeter

Perception of Perimeter

Perimeter, along with area, are the main two geometric figures measures. Confusing them is frequent, as well as believing that the greater one of them is, the greater the other. Indeed, an enlargement (or a reduction) of a shape make its area grow (or decrease) as well as its perimeter. For example, if a field is drawn on a 1/10,000 scale map, the actual field perimeter can be calculated multiplying the drawing perimeter by 10,000. The real area is 10,0002 times the area of the shape on the map.

Nevertheless there is no relation between the area and the perimeter of an ordinary shape. For example, the perimeter of a rectangle of width 0.001 and length 1000 is slighty above 2000, the perimeter of a rectangle of width 0.5 and length 2 is 5. Both areas equal to 1.

Proclus (Vth century) reported that greek peasants "fairly" parted fields relying on their perimeters. But a field's production is proportional to its area, not to its perimeter: many naive peasants may have got fields with long perimeters but low areas (thus, low crops).