First examined by Jacob Bernoulli (1654 - 16705) in 1694, the lemniscate of Bernoulli has the general form of a figure eight, or the mathematical symbol for infinity. Bernoulli's conceptualization of the lemniscate followed his earlier research on parabolas, logarithmic spirals, and epicycloids. Bernoulli originally termed the curve lemniscus, which is Latin for "a pendant ribbon," to describe the unique shape of the curve. Roughly defined, the lemniscate of Bernoulli is the infinite set of all points (called a locus) satisfying the property that the product of the distances between the point and two foci separated by 2a is exactly a². In other words, if (a,0) and (-a,0) are the two foci of the curve, each point (x,y) along the curve satisfies the condition that sqrt[(x - a)² + (y - 0)²)] * sqrt[(x - (-a))² + (y - 0)²) = a². This stipulation is expressed here in...