piNotation

piNotation is a proposed notational framework for expressing the mathematical constant pi in its various representations. It is designed to cover decimal expansions, different base representations, continued fractions, infinite products, and convergent series within a single, machine-readable syntax. The goal is to facilitate comparison, computation, and teaching by providing a uniform way to specify both the representation method and the parameters that govern accuracy or form.

In piNotation, expressions specify a method and parameters rather than a fixed form. Examples include: piNotation(base=10, digits=5) = 3.14159; piNotation(series=Leibniz, terms=1000) ≈ 3.1415926535; piNotation(cf=Convergent, depth=6) = [4; 1, 2, 1, 1, 4, 1]. Other supported modes include products, such as piNotation(product=Wallis, terms=200) ≈ 3.14159, and digit-block representations like piNotation(blocks=2, digits-per-block=5) = 3.1415 92653.

Adoption of piNotation varies by community; it is discussed in mathematical pedagogy and computer science contexts as a tool to annotate and interchange pi representations, rather than a universally adopted standard. Potential benefits include clearer documentation of how a value was obtained and easier automated testing of numerical algorithms.

See also: pi, continued fraction, Leibniz formula for pi, Wallis product, numerical analysis, notational systems.