Trefoil Knot formula A (OpenSCAD)
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Use this formula to make a trefoil knot.
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Mathematics, often called the "language of the universe," is a realm of astounding beauty and wonder, where simple numbers and patterns can unlock profound insights into the world around us, revealing intricate structures in nature, predicting complex phenomena, and even inspiring artistic creation through its inherent symmetry and order.
Here, using this OpenSCAD program to create Trefoil Knots, you can explore the use of sin and cos functions to create shapes you never dreamed of.
Trefoil knots are described here: https://en.wikipedia.org/wiki/Trefoil_knot
On that Wikipedia trefoil page, the first set of formula is:
x=sin t + 2sin 2t
y=cos t - 2cos 2t
z=-sin 3t
When t is incremented from 0 to 360, a closed path is created that is the trefoil knot.
The OpenSCAD program is called “trefoil-knot-A.scad”. Use it to generate a trefoil knot based on a set of parameters. I tried different parameters and came up with 9 different trefoil knots that I like. Demo #1 is the basic trefoil knot. You can try other parameters to create your own trefoil knots.
The OpenSCAD program can also be used to make a tag to show the formula used to create each trefoil knot.
Please post the wonders you find in your exploration.
See:
Trefoil Knot formula A this one
Trefoil Knot formula B
Trefoil Knot formula C