Main Page | See live article | Alphabetical index In mathematics, a lemniscate is a type of curve described a Cartesian equation of the form (x² + y²)² = a²(x² - y²). It resembles the figure '8' on its side. The curve has become a symbol of infinity and is widely used in math. The lemniscate was first described in 1694 by Jakob Bernoulli as a modification of an ellipse (an ellipse is the locus of points which are equidistant from two given points, i.e. the sum of the two distances is constant for all points on an ellipse, but in the case of the lemniscate, the product of these distances is constant). He called it the lemniscus, which is Latin for 'pendant ribbon'. Polar equation: r² = a²cos2φ. Bipolar equation: rr' = a²/2. This article is from Wikipedia. All text is available under the terms of the GNU Free Documentation License.