u/ArjenDijks

I’ve been exploring ways to visualize radical sequences similar to the Spiral of Theodorus.

By using a circle as a locus, you can map all square roots onto a single arc using perfectly even, linear steps along the x-axis.

Because the chord scales linearly with the diameter, we can "calculate" roots by just moving along a grid.

Interactive model: GeoGebra Animation

Questions: Has anyone seen this "chained chord" method used in historical drafting or nomography? Could this be extended to higher-order roots using other conic sections?

Full derivation/discussion on MSE: How to map square roots as a linear progression on a circle?