Fig8

Fig8 is a stylized term used across different disciplines to denote motifs associated with a figure-eight shape. It is not a single entity but a designation found in mathematics, knot theory, and branding or product naming, where the eight-shaped motif is a common visual cue.

In mathematics, the figure-eight curve, or lemniscate, is a planar curve with two lobes that meet at a central crossing. The Bernoulli lemniscate is a well-known example often described by equations such as (x^2 + y^2)^2 = a^2 (x^2 - y^2) or, in polar coordinates, r^2 = a^2 cos(2θ). The curve serves as a classical object in geometry and analysis, appearing in teaching, complex analysis, and dynamical systems studies.

In knot theory, the figure-eight knot, sometimes denoted as 4_1, is the simplest nontrivial knot after the trefoil in standard knot tables. It is a hyperbolic knot, and its complement in three-dimensional space has a finite hyperbolic volume. The figure-eight knot is a common example used to illustrate knot invariants such as the Alexander polynomial and the Jones polynomial, and it helps demonstrate properties of knot complements and hyperbolic geometry.

Beyond mathematics, Fig8 is used in branding and product naming to evoke symmetry, balance, or the visual cue of an eight-shaped form. It may appear in logos, hardware or software model names, or design motifs, with meaning varying by context.

See also: figure-eight, lemniscate, 4_1 knot.