next curve  previous curve  2D curves  3D curves  surfaces  fractals  polyhedra 
SQUARE KNOT, GRANNY KNOT
Two versions of the square knot.
Traditional knots.
Other names of the square knot: reef knot; other names of the granny knot: pigtail knot. Wikipedia: reef knot, granny knot. Images made by Alain Esculier. 
View from above:
(hypotrochoid
with 4 branches in which the first circular motion was replaced by an elliptic
one).
To get the square knot in 3D, take , and for the granny knot . 
square knot 

The open square (on the left) and granny (on the right) knots are the knots with 6 crossings represented opposite.  
If the free blades with different colors are connected, we get the mathematical square and granny knots. 


The first one is the sum of two trefoil
knots mirror images of one another, the second is the sum of two trefoil
knots that have the same orientation.
They are the composite knots with the minimal number of crossings. 


next curve  previous curve  2D curves  3D curves  surfaces  fractals  polyhedra 
© Robert FERRÉOL 2019