The new pi formula refers to various mathematical approaches or discoveries related to the calculation of the value of pi (π). One notable advancement is the development of algorithms that improve the efficiency and accuracy of pi computation. These formulas often involve infinite series, products, or integrals that converge to pi. For example, formulas such as the Bailey-Borwein-Plouffe (BBP) formula allow for the calculation of pi to millions or even billions of digits with remarkable efficiency. Other methods include the use of Chudnovsky algorithms, which utilize complex numbers and rapidly converge to pi. Additionally, there are ongoing explorations in mathematical properties and alternate representations of pi, including geometric interpretations and topological approaches. Such developments contribute to both theoretical mathematics and practical applications in various fields, from engineering to computer science. These breakthroughs not only enhance the understanding of pi but also facilitate advancements in computational techniques and numerical approximations.