Zhang Extrapolation Formulas From Two Points Applied to Years 1944 and 1971 With 2025, 2052, 2079, and 2106 Predicted

In this paper, Zhang extrapolation formulas (ZEF) from two points (named after Yunong Zhang, the principal investigator of the systematic researches on extrapolation, encouraging scholars as well to propose their new extrapolation formulas via different methods) are proposed, investigated, and utilized both forward and backward. Numerical experiments are conducted to validate the accuracy of the ZEF in approximating some functions, yielding relatively satisfactory and interesting results. Besides, we offer a proof of ZEF by utilizing Lagrange interpolation polynomials. Moreover, based on the important two time points, i.e., years 1944 and 1971, using the ZEF forward and backward, many historical years and significant events are coincidentally validated, affirming the accuracy and reliability of the ZEF. Finally, the ZEF are employed to predict the years of potential future events, obtaining the interesting and meaningful years 2025, 2052, 2079, and 2106.