trisectrix of Longchamps

The trisectrix of Longchamps curve is a cubic ¹⁾, which is also named the (equilateral) trefoil.

The curve is an epi spiral.

Longchamps studied the curve in 1888.

notes

1) With equation x (x² - 3y²) = x² + y².

2) To be distinguished from the quartic trefoil