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 = a 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.