Planimetry
Under planimetry is generally understood metric problems of flat geometry , in particular the surface area calculation in the plane. (To calculate the area in the room, see stereometry .)
The area of simple surfaces in the plane can be calculated from known length values. The calculation of more complicated areas is mostly achieved by breaking them down into areas that are easier to calculate. Irregular surfaces , such as B. the area of a maple leaf must be calculated analytically with the curve integral - if the curve is analytically available - estimated using planimetric methods or planimetrised (measured).
The example of a maple leaf clearly shows that abstraction and approximation methods are involved. It is not the (upper) surface of the (not flat) maple leaf that is calculated planimetrically, but the abstracted surface, which its (mathematically imagined) floor plan occupies on the paper. Physically, however, the paper is not flat either and the surface would have to be calculated stereometrically as a surface, but there are huge caves and mountains, fractal fissures even before the accuracy in the nano range, so that one almost comes across the "quantum question" of whether because the surface of a maple leaf is really finite.
See also
- Triangular face
- Polygon - Regular Polygons and Special Polygons section
- Circle (Geometry) - Section of the circle area and parts of the circle