I've been tinkering with drawings of Triquetras (triangular figures composed of three overlapping arcs), and wondering why this ancient symbol has appeared in so many cultures over so many ages.
It occurred me that perhaps some mathematical ratio gives this symbol its harmonious appearance.
I drew a triquetra using the Golden Ratio, i.e., 1.6108 : 1, or (sqrt(5) + 1)/2, and found that it is possible to incorporate this ratio in its construction. I've attached the figure below (apologies for its crude appearance), and it does seem to work:
I'm just wondering if anyone else is familiar with the use of the Golden ratio in the construction of a triquetra, or if the inner triangle where the three lenses meet should be equilateral (i.e., form a Reuleaux triangle). The inner triangle of a triquetra based on the Golden ratio is not a Reuleaux triangle; rather, it is an isosceles triangle.
Any helpful comments would be greatly appreciated.