# Help creating an Arithmetic Rope using circles and moveable points

I am trying to create a model of the Arithmetic Rope (13 knot rope - Arithmetic rope - Wikipedia) using Desmos but since this is my first attempt at starting from scratch, I need help!!

Here is what I am thinking: I would like to represent the knots by moveable points so that the students can manipulate the rope to discover one set of the Pythagorean Triple. That being said, I need the distance between each knot (moveable point) to be exactly the same. After a few different attempts, I concluded that I’d need to create a number of circles with the knots being the centers of the circles while the distance between the knots represents equal radii. (Note: I may be wrong in my approach so any other suggestions are welcomed!)

I started by creating 3 moveable points (A, B, & C) and 2 circles (with centers A and B respectively). How do I make distance AB = distance BC?

Here is my draft: Modeling Arithmetic Rope - Draft • Activity Builder by Desmos
I figured that if I can create the first 2 circles (then hide them leaving only the radii visible), I can follow the same steps to construct the rest of the rope.

I’d appreciate any help with this.

Here is something similar done with GeoGebra if it makes it easier to see what I’m attempting to create: The 13 knot rope – GeoGebra

Here’s a quick attempt using some parametric equations. It doesn’t work quite like the Geogebra activity, but it’s pretty close. It can be polished up more, so let me know if you need any help finishing it up!

Thank you so much!
I was able to finish it (slide 2 of my draft: )

I believe it will do the job as is but open to suggestions if you have any