Examples of knots drawn using Maple

Modified by :- Rohit Chaudhary

Run these commands first

> with(plots,tubeplot): with(algcurves,plot_knot):

The Unknot

> unknot:=tubeplot([cos(t),sin(t),0,t=0..2*Pi],orientation=[60,40],radius=0.2,scaling=constrained):

> unknot;

The Trefoil Knot

> trefoil:=tubeplot([ -10*cos(t) - 2*cos(5*t) + 15*sin(2*t),
-15*cos(2*t) + 10*sin(t) - 2*sin(5*t), 10*cos(3*t),
t= 0..2*Pi],
orientation=[60,0]):

> trefoil;

The Figure8 Knot

> figure8:=tubeplot([32*cos(t) - 51*sin(t) - 104*cos(2*t) - 34*sin(2*t) + 104*cos(3*t) - 91*sin(3*t), 94*cos(t) + 41*sin(t) + 113*cos(2*t) - 68*cos(3*t) - 124*sin(3*t), 16*cos(t) + 73*sin(t) - 211*cos(2*t) - 39*sin(2*t) - 99*cos(3*t) - 21*sin(3*t),t=0..2*Pi],radius=20,tubepoints=8,numpoints=100,orientation=[111,-95],scaling=constrained):

> figure8;

Five Crossing knots

> tubeplot([88*cos(t) + 115*sin(t) - 475*cos(2*t) - 127*sin(2*t) - 87*cos(3*t) + 36*sin(3*t) + 11*cos(4*t) - 19*sin(4*t), 89*cos(t) - 32*sin(t) - 172*cos(2*t) + 294*sin(2*t) + 76*cos(3*t) + 102*sin(3*t) - 61*cos(4*t) + 113*sin(4*t), 44*cos(t) - 69*sin(t) + 34*cos(2*t) + 223*sin(2*t) + 16*cos(3*t)+ 120*sin(3*t) + 42*cos(4*t) - 125*sin(4*t),
t=0..2*Pi], radius=25,numpoints=100);

> tubeplot([- 33*cos(t) + 43*sin(t) + 214*sin(2*t) - 101*cos(3*t) - 47*sin(3*t) + 11*sin(4*t),- 57*cos(t) + 99*sin(t) - 54*cos(2*t) - 159*sin(2*t) - 117*cos(3*t) - 5*sin(3*t) - 31*cos(4*t) - 45*sin(4*t),34*cos(t) - 21*sin(t) - 100*cos(2*t) - 93*sin(2*t) - 27*cos(3*t) - 16*sin(3*t) + 52*cos(4*t) + 84*sin(4*t),t=0..2*Pi],radius=25,numpoints=100);

Six Crossing knots

> tubeplot([12*cos(t) + 20*sin(t) - 163*cos(2*t) + 76*sin(2*t) - 87*cos(3*t) - 15*sin(3*t) - 21*cos(4*t) + 14*sin(4*t) +
24*cos(5*t) - 50*sin(5*t), 29*cos(t) + 78*sin(t) - 180*cos(2*t) + 58*sin(2*t) + 88*cos(3*t) + 72*sin(3*t) - 14*sin(4*t), - 30*cos(t) - 78*sin(t) - 111*cos(2*t) + 37*sin(2*t) - 67*cos(3*t) - 51*sin(3*t) + 31*cos(4*t) + 8*sin(4*t) -
11*cos(5*t) + 65*sin(5*t),t=0..2*Pi], radius=25, numpoints=100);

> tubeplot([- 6*cos(t) - 21*sin(t) - 195*cos(2*t) + 92*sin(2*t) - 64*cos(3*t) - 23*sin(3*t) - 6*cos(4*t) + 13*sin(4*t) + 24*cos(5*t) + 15*sin(5*t) + 41*sin(6*t)
,21*cos(t) - 24*sin(t) - 207*cos(2*t) - 72*sin(2*t) + 112*cos(3*t) - 7*sin(3*t) - 13*cos(4*t) - 40*sin(4*t) - 27*cos(5*t) - 3*sin(5*t) - 17*cos(6*t) ,- 18*cos(t) - 13*sin(t) + 113*cos(2*t) - 107*sin(2*t) + 86*cos(3*t) - 9*sin(3*t) - 26*cos(4*t) - 7*sin(4*t) + 24*cos(5*t) + 33*sin(5*t) + 21*cos(6*t) + 31*sin(6*t),t=0..2*Pi],radius=25,numpoints=100);

> tubeplot([- 40*cos(t) + 32*sin(t) + 69*cos(2*t) - 12*sin(2*t) + 120*cos(3*t) - 52*sin(3*t) - 56*cos(4*t) + 46*sin(4*t) -17*sin(5*t) + 14*cos(6*t) + 19*sin(6*t), 90*cos(t) + 89*sin(t) - 142*cos(2*t) + 147*sin(2*t) + 74*cos(3*t) + 85*sin(3*t) - 56*sin(4*t) + 23*cos(5*t) + 16*cos(6*t) + 7*sin(6*t), 52*cos(t) + 64*sin(t) + 53*cos(2*t) + 35*sin(2*t) + 77*cos(3*t) - 87*sin(3*t) + 101*cos(4*t) - 19*sin(4*t) - 5*cos(5*t) + 2*sin(5*t) + 3*cos(6*t) + 9*sin(6*t),t=0..2*Pi],radius=25,numpoints=100);

A Funny looking Knot

> Funny:=tubeplot([ - 22*cos(t) - 128*sin(t) - 44*cos(3*t) - 78*sin(3*t),
- 10*cos(2*t) - 27*sin(2*t) + 38*cos(4*t) + 46*sin(4*t),
70*cos(3*t)-40*sin(3*t),t=0..2*Pi],orientation=[-90,90],radius=10,tubepoints=12,numpoints=100):

> Funny;

Another funny looking Knot

> Square:=tubeplot([- 22*cos(t) - 128*sin(t) - 44*cos(3*t) - 78*sin(3*t), 11*cos(t) - 43*cos(3*t) + 34*cos(5*t) - 39*sin(5*t) , 70*cos(3*t) - 40*sin(3*t) + 8*cos(5*t)- 9*sin(5*t), t=0..2*Pi],radius=10,tubepoints=12,numpoints=100):

> Square;

Star Knot

> f:=(y^2-3*x^5);
plot_knot(f,x,y,epsilon=0.8,radius=0.2,style=patch,tubepoints=12,orientation=[60,0]);

A Nice Link

> f:=(y^3-x^7)*(y^2-2*x^5);
plot_knot(f,x,y,epsilon=0.8,radius=0.1,style=patch, tubepoints=12,orientation=[60,0]);

Two projections of the same Link.

> g:=(y^3-x^7)*(y^2-2*x^5)+y^3;

> plot_knot(g,y,x,epsilon=0.8);

> plot_knot(g,x,y,epsilon=0.8);

>