similitudes

Similitude, and its plural similitudes, denotes likeness or resemblance. In mathematics, a similitude is a similarity transformation: a map that preserves shapes while possibly changing size. It preserves angles and maps lines to lines; distances are scaled by a fixed nonzero factor k, called the similarity ratio. If k > 0 the orientation is preserved; if k < 0, orientation is reversed. Every two-dimensional similitude can be represented as a rotation or reflection, followed by a uniform scaling about a point, and a translation. Equivalently, f(x) = a + k R(x) for a fixed point a, a scale k, and an orthogonal transformation R. Two figures are similar when one can be obtained from the other by a similitude; their corresponding sides are proportional, corresponding angles are equal, and areas scale by k^2. The term distinguishes from congruence, where k = ±1.

The word comes from Latin similitudo, meaning “likeness.”

In general usage, similitude means resemblance or likeness; in literature it can refer to an analogy or figurative comparison, and in science or philosophy it may describe resemblances among phenomena due to shared features. The concept emphasizes structural similarity rather than exact size, allowing comparisons across different contexts while remaining neutral and descriptive.