Lissajous-toric knotFrom Wikipedia, the free encyclopedia In knot theory, a Lissajous-toric knot is a knot defined by parametric equations of the form: Lissajous-toric knot with parameters 5, 6 and 22 in braid form (with z-axis in horizontal direction) x ( t ) = ( 2 + sin q t ) cos N t , y ( t ) = ( 2 + sin q t ) sin N t , z ( t ) = cos p ( t + ϕ ) , {\displaystyle x(t)=(2+\sin qt)\cos Nt,\qquad y(t)=(2+\sin qt)\sin Nt,\qquad z(t)=\cos p(t+\phi ),} where N {\displaystyle N} , p {\displaystyle p} , and q {\displaystyle q} are integers, the phase shift ϕ {\displaystyle \phi } is a real number and the parameter t {\displaystyle t} varies between 0 and 2 π {\displaystyle 2\pi } .[1] For p = q {\displaystyle p=q} the knot is a torus knot.
In knot theory, a Lissajous-toric knot is a knot defined by parametric equations of the form: Lissajous-toric knot with parameters 5, 6 and 22 in braid form (with z-axis in horizontal direction) x ( t ) = ( 2 + sin q t ) cos N t , y ( t ) = ( 2 + sin q t ) sin N t , z ( t ) = cos p ( t + ϕ ) , {\displaystyle x(t)=(2+\sin qt)\cos Nt,\qquad y(t)=(2+\sin qt)\sin Nt,\qquad z(t)=\cos p(t+\phi ),} where N {\displaystyle N} , p {\displaystyle p} , and q {\displaystyle q} are integers, the phase shift ϕ {\displaystyle \phi } is a real number and the parameter t {\displaystyle t} varies between 0 and 2 π {\displaystyle 2\pi } .[1] For p = q {\displaystyle p=q} the knot is a torus knot.