Lemniscia

A lemniscate (plural: lemniscates or lemniscia) is a figure-eight shaped curve. The term "lemniscate" often refers to the specific lemniscate of Bernoulli, but it can also describe other similar curves. The word derives from the Latin "lemniscatus" meaning "decorated with ribbons," referring to ribbons tied in loops.

In mathematics, lemniscates are frequently encountered as algebraic curves defined by polynomial equations. The lemniscate of Bernoulli is defined by the equation (x² + y²)² = a²(x² - y²), where 'a' is a constant determining the size of the lemniscate.

Beyond the lemniscate of Bernoulli, various other curves share the figure-eight or infinity-symbol shape and are also referred to as lemniscates. Examples include the lemniscate of Gerono and the hippopede (also known as Booth's lemniscate). Each lemniscate type has a unique defining equation and geometric properties.

The lemniscate shape has found application in various fields, including mathematics, physics, and design. Its elegant and symmetrical form makes it a visually appealing motif.