strophoid

[ strof-oid, stroh-foid ]

noun

, Geometry.

1. a plane curve generated by the loci of points p and pprime; on a straight line that intersects the y-axis at a point n and the minus x-axis at a fixed point q, such that pn = npprime; = on, as on changes, where o is the origin. Equation: y 2 = x 2 ( x + a )/( a − x ).

strophoid

/ strō′foid′ /

1. The curve traced out by points P and P ′ which lie on lines through a fixed point A where the midpoint M of PP ′ is on a fixed line and the absolute value ‖ PM ‖ equals the absolute value ‖ P ′ M ‖ equals the absolute value ‖ MO ‖, where O is the projection of A onto that fixed line.

Word History and Origins

Origin of strophoid¹

1875–80; < Greek stróph ( os ) twine + -oid, modeled on French strophoïde