PEMAHAMAN SISWA SMP DALAM EFISIENSI ALGORITMA SARINGAN ERASTOTHENES

indonesia

Authors

  • Devina Shafira Maharani Universitas Negeri Padang, Indonesia
  • Yulyanti Harisman Universitas Negeri Padang, Indonesia

DOI:

https://doi.org/10.34125/jkps.v9i1.116

Keywords:

Matematika, Bilangan Prima, Saringan Erastothenes, Pemahaman Siswa

Abstract

The logic of shape, number, and sequence is the subject of mathematics. We use mathematics in everything we do. Available everywhere. Everything we use every day—computers, software, hardware, art, money, engineering, sports, and even ancient and modern architecture is built around it. In the realm of number theory, mathematicians study various aspects of prime numbers, including the distribution of prime numbers, ordering patterns of prime numbers, and methods for generating prime numbers. Even the most ancient and rudimentary societies used mathematics, and since the beginning of history, mathematical discoveries have been made. at the forefront of every civilized civilization. This is simple but can be applied to many phenomena in everyday life, making an Ancient Greek mathematician from the Hellenestic era named Erastothenes successful in being the person who created an extraordinary discovery, namely, the Erastothenes Sieve. Therefore, the aim of this research is to provide encouragement to junior high school students to understand and be interested in studying mathematics, especially the Erastothenes measurement method and then apply it in everyday life. This type of research is qualitative research with a descriptive approach and literature review method. The instruments used in this research are tests, interviews and documentation. The results of this research show the level of students' understanding of the Sieve of Eratosthenes.

References

Bengelloun, S. A. (1986). An incremental primal sieve. Acta informatica, 23, 119–125.

Bokhari. (1987). Multiprocessing the Sieve of Eratosthenes. Computer, 20(4), 50–58. https://doi.org/10.1109/MC.1987.1663535

Crandall, Richard, & Pomerance, Carl. (2001). Prime numbers. A computational perspective. New York: Springer-Verlag. Cecilia, M. (2023, May 31). Biografi Eratosthenes, ahli matematika dan geografi Yunani. YuBrain. https://www.yubrain.com/id/sastra/biografi-eratostees/

Dickson, L. E. (1930). Introduction to the theory of numbers (Chicago University Press, 1929 : Introduction).2. Studies in the theory of numbers (Chicago University Press, 1930 : Studios). 3. History of the theory of numbers (Carnegie Institution; vol. i, 1919; vol. ii, 1920; vol. iii, 1923: History).

Diodati, M. (2021). The Sieve of Eratosthenes. Not Zero. https://medium.com/not-zero/the-sieve-of-eratosthenes-2ba82a50d09d

Estermann, T. (1952). Introduction to Modern Prime Number Theory Cambridge Tracts in’ Mathematics. 41.

R. Fueter, R. (1950). Synthetische ZahEentheorie. Berlin. de Gruyter.

Harahap, M. K., & Khairina, N. (2019). The Comparison of Methods for Generating Prime Numbers between The Sieve of Eratosthenes, Atkins, and Sundaram. Sinkron : Jurnal Dan Penelitian Teknik Informatika, 3(2), Article 2. https://doi.org/10.33395/sinkron.v3i2.10129

Hardy, G. H., & Wright, E. M. (1979). An introduction to the theory of numbers.

th edn. Clarendon Press. Pages 354–358.

Kochar, V., Goswami, D. P., Agarwal, M., & Nandi, S. (2016). Contrast various tests for primality. 2016 International Conference on Accessibility to Digital World (ICADW), 39–44. https://doi.org/10.1109/ICADW.2016.7942510

Lejeune, D, P. G. (1894) Vorlesungen über Zahlentheorie, herausgegeben

von R. Dedekind (4th edition, Braunschweig, Vieweg,).

Mark, J. J. (2022). Eratosthenes. World History Encyclopedia. https://www.worldhistory.org/Eratosthenes/

Marlina, W., & Jayanti, D. (2019). 4c Dalam Pembelajaran Matematika Untuk Menghadapi Era Revolusi Industri 4.0.

Martinez (B.S.), C. (2023, May 31). Biografi Eratosthenes, ahli matematika dan geografi Yunani. YuBrain. https://www.yubrain.com/id/sastra/biografi-eratostees/

Mazur, B., & Stein, W. (2016). Prime Numbers and the Riemann Hypothesis. Cambridge University Press.

Meertens, Lambert. (2004). Calculating the Sieve of Eratosthenes. Journal of

functional programming, 14(6), 759–763

Miller, G. A. (1928). The So-Called Sieve of Eratosthenes. Science, 68(1760), 273–274. https://doi.org/10.1126/science.68.1760.273.b

Pritchard, Paul. (1987). Linear prime-number sieves: A family tree. Science of

computer programming, 9, 17–35.

Rusandi, & Rusli, M. (2021). Merancang Penelitian Kualitatif Dasar/Deskriptif dan Studi Kasus. Al-Ubudiyah: Jurnal Pendidikan dan Studi Islam, 2(1), 48–60. https://doi.org/10.55623/au.v2i1.18

Murty, M. R., & Saradha, S. (1987a). On the Sieve of Eratosthenes. Canadian Journal of Mathematics, 39(5), 1107–1122. https://doi.org/10.4153/CJM-1987-056-8

Oh, Jun-Young. (2017). Understanding the Estimation of Circumference of the Earth by of Eratosthenes based on the History of Science, For Earth Science Education. Journal of the Korean Society of Earth Science Education, 10(2), 214–225. https://doi.org/10.15523/JKSESE.2017.10.2.214

O’Neill, M. E. (2009). The Genuine Sieve of Eratosthenes. Journal of Functional Programming, 19(1), 95–106. https://doi.org/10.1017/S0956796808007004

Sieve of Eratosthenes: A Powerful Tool for Identifying Composite Numbers. (n.d.). FasterCapital. Retrieved January 13, 2024, from https://fastercapital.com/content/Sieve-of-Eratosthenes--A-Powerful-Tool-for-Identifying-Composite-Numbers.html

Subadi, T. (2006). Metode penelitian kualitatif. Muhammadiyah University Press. https://publikasiilmiah.ums.ac.id/bitstream/handle/11617/9298/5.%20Metode%20%20Penel.%20Kualitatif.pdf?sequence=1

Wang, X. (2021). The Genesis of Prime Numbers—Revealing the Underlying Periodicity of Prime Numbers. Advances in Pure Mathematics, 11(01), 12–18. https://doi.org/10.4236/apm.2021.111002

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Published

2024-03-30

How to Cite

Maharani, D. S., & Harisman, Y. (2024). PEMAHAMAN SISWA SMP DALAM EFISIENSI ALGORITMA SARINGAN ERASTOTHENES: indonesia. Jurnal Kepemimpinan Dan Pengurusan Sekolah, 9(1), 115–126. https://doi.org/10.34125/jkps.v9i1.116

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