Apollonian

Apollonian is an adjective that derives from Apollo, the ancient Greek god, and, in scholarly use, from Apollonius of Perga, a Greek geometer. It is used to describe things related to Apollo or embodying traits associated with him, such as harmony, order, and beauty.

In philosophy and aesthetics, Apollonian refers to the rational, structured, and form-driven aspect of experience or art, as opposed to the Dionysian, which emphasizes chaos, passion, and intoxication. The distinction originates with Friedrich Nietzsche in The Birth of Tragedy and has been applied in literary criticism and cultural theory to analyze styles and movements that favor form, clarity, and restraint.

In geometry, Apollonian relates to Apollonius of Perga, who studied circles and conics in ancient Greece. The circle of Apollonius is the locus of points for which the distances to two fixed points are in a constant ratio. The Apollonius problem asks for a circle tangent to three given circles, a classic construction in Euclidean geometry. Related concepts include Apollonian circles and the Apollonian gasket, a fractal packing generated by repeatedly filling the interstices between mutually tangent circles with new tangent circles; the gasket is named for its association with the circle-tangent problems studied by Apollonius.