Efficient Computation of Number Fractions from the Square Root of Two Using the A-B Goen Number Function Via the Ivan Newton (in) Series
DOI:
https://doi.org/10.21512/emacsjournal.v6i3.11575Keywords:
Numbers, Functions, Square Root of Two, Irrational NumbersAbstract
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.
Plum Analytics
References
Goenawan, Stephanus Ivan. (2020). Comparison Simulation Analysis Of The Gradual Summation Of A Function With Recognition Of Direct Extrapolation Via IN Series. IJASST Univ. Sanata Dharma, Yogyakarta.
Goenawan, Stephanus Ivan. (Januari 2022). Fractional Generating Function from The Square Root of Two with A-B Goen Numbers, Engineering, Mathematics, and Computer Science (EMACS) Journal, Vol. 4 No. 1. hal 11 – 14, e-ISSN: 2686-2573.
Goenawan, Stephanus Ivan. (Januari 2021). Order Theory I And II As Foundations For Finding Relationship Between Formulas, Engineering, Mathematics, and Computer Science (EMACS) Journal, Vol. 2 No. 1. hal 1 – 4, p-ISSN 1410-2765.
Gel'fand, Izrael M.; Shen, Alexander. (2023). Algebra (8rd ed.). Birkhäuser. p. 120. ISBN 0-8176-3677-3.
Lord, Nick. (November 2008). "Maths bite: irrational powers of irrational numbers can be rational", Mathematical Gazette 92. p. 534.
Marshall, Ash J., and Tan, Yiren. (March 2012). "A rational number of the form aa with a irrational", Mathematical Gazette 96. pp. 106-109.
Mitchell, Douglas W. (November 2003). "Using Pythagorean triples to generate square roots of I2", Mathematical Gazette 87. 499–500.
Krantz, Steven George (2006). Calculus: Single Variable, Volume 1. Springer Science & Business Media. p. 248. ISBN 978-1-931914-59-8.
McQuarrie, Donald A. (2003). Mathematical Methods for Scientists and Engineers, University Science Books. ISBN 978-1-891389-24-5
Salas, Saturnino L.; Hille, Einar; Etgen, Garret J. (2007). Calculus: One and Several Variables (10th ed.). Wiley. ISBN 978-0-471-69804-3.
Stewart, James (2012). Calculus: Early Transcendentals, 7th ed., Brooks Cole Cengage Learning. ISBN 978-0-538-497 90-9
Thomas, George B., Maurice D. Weir, Joel Hass, Frank R. Giordano (2008), Calculus, 11th ed., Addison-Wesley. ISBN 0-321-48987-X
Zill, Dennis G.; Wright, Scott; Wright, Warren S. (2009). Calculus: Early Transcenden-tals (3 ed.). Jones & Bartlett Learning. p. xxvii. ISBN 978-0-7637-59957.
Downloads
Published
Issue
Section
License
Copyright (c) 2024 Stephanus Ivan Goenawan
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Authors who publish with this journal agree to the following terms:
a. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License - Share Alike that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
b. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
c. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
USER RIGHTS
All articles published Open Access will be immediately and permanently free for everyone to read and download. We are continuously working with our author communities to select the best choice of license options, currently being defined for this journal as follows: Creative Commons Attribution-Share Alike (CC BY-SA)
