The Cartesian equation to the curve is ${\displaystyle y=x\cot {\tfrac {\pi x}{2a}}}$, which shows that the curve is symmetrical about the axis of y and that it consists of a central portion flanked by infinite branches (fig. 2). The asymptotes are x = ±2na, n being an integer. The intercept on the axis of y is 2a/π; therefore, if it were possible to accurately construct the curve, the quadrature of the circle would be effected. The curve also permits the solution of the problems of duplicating a cube (q.v.) and trisecting an angle.