A lemniscate is a plane curve with a characteristic shape, consisting of two loops that meet at a central point as shown below. The curve is also known as the lemniscate of Bernoulli.
In the (x, y) plane, the lemniscate can be described in terms of the following general equation:
(x 2 + y 2) 2 = 2a 2 (x 2 - y 2)
where a represents the greatest distance between the curve and the origin. There are two points on the curve that meet this criterion; both of them lie on the x axis. In the above graph, if each division represents one unit, then a = 5.
The lemniscate, reduced in size to that of typographical characters, is commonly used as the symbol for infinity, or for a value that increases without limit.