Editing Perimeter (section)

== Perception of perimeter==
{{multiple image
 | image1 = Hexaflake.gif
 | caption1 = The more one cuts this shape, the lesser the area and the greater the perimeter. The [[convex hull]] remains the same.
 | image2 = Neuf Brisach.jpg
 | caption2 = The [[Neuf-Brisach]] fortification perimeter is complicated. The shortest path around it is along its [[convex hull]].
 | total_width = 400
 | align = right
}}
{{Main|Area (geometry)|convex hull}}
The perimeter and the [[area (geometry)|area]] are two main measures of geometric figures. Confusing them is a common error, as well as believing that the greater one of them is, the greater the other must be. Indeed, a commonplace observation is that 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/{{formatnum:10000}} scale map, the actual field perimeter can be calculated multiplying the drawing perimeter by {{formatnum:10000}}. The real area is {{formatnum:10000}}{{sup|2}} 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 slightly above 2000, while the perimeter of a rectangle of width 0.5 and length 2 is 5. Both areas are equal to 1.

[[Proclus]] (5th century) reported that Greek peasants "fairly" parted fields relying on their perimeters.{{r|heath}} However, a field's production is proportional to its area, not to its perimeter, so many naive peasants may have gotten fields with long perimeters but small areas (thus, few crops).

If one removes a piece from a figure, its area decreases but its perimeter may not. The convex hull of a figure may be visualized as the shape formed by a rubber band stretched around it.{{r|convexhull}} In the animated picture on the left, all the figures have the same convex hull; the big, first [[hexagon]].