omoteties

Omotety is a geometric transformation. It is a type of dilation where all points are mapped from a fixed center point by a constant scalar factor. This means that the size of an object is scaled up or down, but its shape remains the same. The direction from the center point to each point on the object is preserved. If the scalar factor is greater than 1, the object is enlarged. If the scalar factor is between 0 and 1, the object is reduced. If the scalar factor is 1, the object remains unchanged. If the scalar factor is negative, the object is inverted through the center point as well as scaled. The center of homothety is a point that remains fixed under the transformation. All lines passing through the center of homothety are invariant under the transformation. Omotety is also known as dilation or scaling. It is a fundamental concept in Euclidean geometry and has applications in various fields, including art, architecture, and computer graphics. In essence, an omotety produces a similar figure to the original.