A calculational approach to path-based properties of the EisensteinStern and SternBrocot trees via matrix algebra
This paper proposes a calculational approach to prove properties of the EisensteinStern and the SternBrocot trees. The calculational style of reasoning is enabled by a matrix formulation well-suited to formulate path-based properties. We show that nodes with palindromic paths contain the same rational in both the EisensteinStern and SternBrocot trees. We show how certain numerators and denominators in these trees can be written as the sum of two squares. We show how we can construct Sierpinski's triangle from these trees of rationals.
sternbrocot tree eisensteinstern tree (aka calkinwilf tree) calculational method euclid's algorithm sierpi?ski's triangle rational number