Efficient Computation of Number Fractions from the Square Root of Two Using the A-B Goen Number Function Via the Ivan Newton (in) Series

Goenawan, Stephanus Ivan

Engineering, Mathematics and Computer Science Journal (EMACS)
Vol. 6 No. 3 (2024): EMACS

The square root number of two is an irrational number. If it is an irrational number, the result cannot be written as a fraction of the numerator and denominator. Fractions that approach the square root value of two have a correlation with Goen's A-B numbers. The regularity of the A-B Goen number sequence can be formulated into the A-B Goen function which is built from the Ivan Newton series. In this research, it can be proven that the A-B Goen function from the Ivan Newton (IN) series is computationally more effective and efficient when compared to the A-B Goen generating function in producing A-B Goen numbers which in infinite sequence will approach the square root value of two.