Making it simple:
deleting a pair of vertices:
cutting the new edges - starting from 2 and adding one for each new cut: 2,3,4,5,...
Now, applying Circularise [RMB] for each group of edges cut:
Something "magic" happened here... The value I used for circularise in order to get the edges laying over the curve is a Fibonacci number too: 89°! 
deleting a pair of vertices:cutting the new edges - starting from 2 and adding one for each new cut: 2,3,4,5,...Now, applying Circularise [RMB] for each group of edges cut:Something "magic" happened here... The value I used for circularise in order to get the edges laying over the curve is a Fibonacci number too: 89°!