Scaling Geometry: Geometry, Euclidean Isotropy, Linear Map, Scale Factor, Homothetic Transformation, Similarity Anisotropy, Ratio, Map

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In Euclidean geometry, uniform scaling or isotropic scaling is a linear transformation that enlarges or increases or diminishes objects; the scale factor is the same in all directions; it is also called a homothety. The result of uniform scaling is similar, in the geometric sense to the original. A scale factor of 1 is normally allowed, so that congruent shapes are also classed as similar, but some school text books specifically exclude this possibility. More general is scaling with a separate scale factor for each axis direction. Non-uniform or anisotropic scaling is obtained when at least one of the scaling factors is different from the others; a special case is directional scaling, in one direction. Non-uniform scaling changes the shape of the object; a rectangle may change into a rectangle of a different shape, but also in a parallelogram, the angles between lines parallel to the axes are preserved, but not all angles.

Pagina's: 100, Paperback, Betascript Publishers