Determining The hypocycloid area By using the
circle of assist

Kurnia Okta Frima; Mashadi; Sri Gemawati

doi:https://doi.org/10.14445/22315373/IJMTT-V66I10P515

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 10 | Year 2020 | Article Id. IJMTT-V66I10P515 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I10P515

Determining The hypocycloid area By using the circle of assist

Kurnia Okta Frima, Mashadi, Sri Gemawati

Abstract

This paper discusses the hypocycloid area, starting with determining the auxiliary circle to determine the hypocycloid area. Furthermore, to determine the hypocycloid area with the auxiliary circle, it is obtained from the reduction of the area of the circle forming the hypocycloid and the area of the auxiliary circle. From determining the hypocycloid area, the hypocycloid area is obtained for n = 3, n = 4, n = 5 and n = 6 and the relationship between the circle that pertains to the hypocycloid and the circle that forms the hypocycloid for all n.

Keywords

Hypocycloid, hypocycloid area, astroid.

References

[1] A. Biran, Geometry for Naval Architect, Technion: Elsevier, Cambridge, 2019.
[2] N. Danarjaya, Schaum’s Outline Kalkulus, Edisi Keempat, Terjemahan dari Schaum’s Outlines of Theory and Problems of Calculus oleh Frank Ayres, Erlangga, Jakarta, 2004.
[3] C. G. Fraser, A historical perspective, Greenwood Publishing Group. United States of America, 2006.
[4] E. Gwin, Hypocycloid and Hypotrocoids, MathAMATYC Educator, 6 (2014), 5-17.
[5] M. H. Hsu, H.S. Yan, J.Y. Liu and L. C. Hsieh, Epicycloid (hypocycloid) mechanisms design, Proceedings of the Internasional Multiconference of Engineers and Computer Scientists, 2 (2008), 19-21.
[6] E. S. Kennedy, Late Medieval Planetary Theory, Isis 57 (1966), 365-378.
[7] Mashadi, Geometri, UR Press, Pekanbaru, 2012.
[8] Mashadi, Geometri Lanjut, UR Press, Pekanbaru, 2015.
[9] H. A. Parhusip, Arts revealed in calculus and its extension, Int. J. Stat. Math., 1 (2014), 16-23.
[10] Purwoto, H.A. Parhusip, T. Mahatma, Perluasan Kurva Parametrik Hypocycloid 2 Dimensi Menjadi 3 Dimensi dengan Sistem Koordinat Bola., Prosiding Seminar Nasional VIII UNNES, 8 (2014), 326-336.
[11] G. Saliba, A History of Arabic Astronomy: Planetary Theoris During the Golden Age of Islam, 1995.
[12] V. Suryaningsih, H. A. Parhusip, T. Mahatma, Kurva Parametrik dan Transformasinya untuk Pembentukan Motif Dekoratif, Prosiding Seminar Nasional Matematika dan Pendidikan Matematika FMIPA UNY, (2013), 249-258.
[13] I. N. Veselovsky, Copernicus and nasir al-Din al-Tusi, Journal for the History of Astronomy, 4 (1973), 128-130.
[14] B. Wang, Generation and Application of Hypocycloid and Astroid, Journal of Physics: Conference series, (2019), 25-32.
[15] J. Wang, X. Ping, The Design Method of Hypocycloid and Apycycloid of Ball Type Speed Reducer, International Research Journal of Advanced Engineering and Science, 4 (2019), 185-187.
[16] E. Yudha, CliffQuickReviewTM Geometry, Terjemahan dari CliffQuickReviewTM Geometry oleh Ed Kohn, Pakar Raya, Bandung, 2003.

Citation :

Kurnia Okta Frima, Mashadi, Sri Gemawati, "Determining The hypocycloid area By using the circle of assist," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 10, pp. 133-139, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I10P515