# W-curve

A W - curve is a geometric curve in a projective space, which is invariant under a 1 -parameter group of projective transformations. W curves were first investigated in 1871 by Felix Klein and Sophus Lie, They gave them their name. For the construction of a W -curve ruler sufficient. Many famous curves are W - curves, such as conic sections, logarithmic spirals, powers (such as y = x3), logarithms and helical ( helix); the trigonometric functions, for example, no W - curves. W - curves are often present in the plant kingdom.

## Naming

The letter ' W' comes from ' throw ', which - according to von Staudt - means a set of four points on a line. A one-dimensional W - curve ( that is, the motion of a point on a straight line projektieven ) is determined by such a series.

"W - curve" sounds a lot like " path - curve", and that can be translated into English as "path curve". Therefore, we find this term often in English literature.