Under planimetry is generally understood metric problems of plane geometry, in particular the area of computation in the plane. (For area calculation in the room see solid geometry. )
The area of simple surfaces in the plane can be calculated from known length values. The calculation of complicated surfaces is usually achieved via decomposition into patches, which can be calculated easily. Irregular surfaces such as the surface of a maple leaf must analytically with the line integral - if the curve is present analytical - calculated, estimated by planimetric methods or planimetriert ( measured ) are.
Here, the example of a maple leaf shows particularly clearly that it is about abstraction and approximation methods. Is calculated by planimetry not the (upper ) surface of the ( non-flat ) maple leaf, but the abstracted surface, which is in its ( mathematically imaginary ) Ground plan on paper. Physically, however, is also the paper is not flat and the surface would have to be calculated as surface stereometrically, but then find themselves before the nanoscale precision huge caves and mountains, fractal Klüftungen that you can about it almost runs on the " quantum question " whether because the surface of a maple leaf is finally real.