Double butterfly theorem on ellips

Mashadi Mashadi; Muhammad Farhan Dinata

doi:10.62918/hjma.v1i1.6

Authors

Mashadi Universitas Riau
Muhammad Farhan Dinata Universitas Riau

DOI:

https://doi.org/10.62918/hjma.v1i1.6

Keywords:

Butterfly Theorem, Double Butterfly Theorem, Haruki's Lemma

Abstract

The butterfly and the double butterfly theorem are applied to a circle. In this paper, we will modify the double butterfly theorem on an ellipse. The method of proving the double butterfly theorem on an ellipse can be done if Haruki’s lemma can apply to any ellipse. Thus, in this paper will also be given a modified Haruki’s lemma on an ellipse.

References

L. Bankoff, The metamorphosis of the butterfly theorem, Mathematics Magazine 60

(1987), 195–210.

Y. Bezverkhnyev, Haruki’s lemma and a related locus problem, Forum Geometricorum 8 (2008), 63–72.

A. Bogomolny, Butterflies in Ellipse: What is it about?, accessed 19 October 2022, https://www.cut-the-knot.org/Curriculum/Geometry/ButterflyInEllipse.shtml.

A. Bogomolny, The Butterfly Theorem, accessed 19 October 2022, https://www.cut-the-knot.org/pythagoras/Butterfly.shtml.

M. Celli, A proof of the butterfly theorem using the similarity factor of the two wings, Forum Geometricorum 16 (2016), 337–338.

Z. Cerin, A generalization of the butterfly theorem from circles to conics, Mathematical Communications 6 (2001), 161–164.

A. D. D. Craik, J. J. O’Connor, Some unknown documents associated with William Wallace (1768-1843), Journal of the British Society for the History of Mathematics 26 (2011), 17–28.

C. Donolato, A proof of the butterfly theorem by an argument from statics, International Journal of Mathematical Education in Science and Technology 48 (2017), 1281–1284.

C. Donolato, A proof of the butterfly theorem using Ceva’s theorem, Forum Geometricorum 16 (2016), 185–186.

L. Hoehn, A new proof of the double butterfly theorem, Mathematics Magazine 64 (1990), 256–257.

D. Jones, A double butterfly theorem, Mathematics Magazine 49 (1976), 86–87.

Mashadi, Geometri, Edisi Kedua, UR Press, Pekanbaru, 2015.

Mashadi, Geometri Lanjut, UR Press, Pekanbaru, 2015.

N. A. Utami, Pengembangan lema Haruki pada elips, accessed 19 October 2022, https://repository.unri.ac.id/handle/123456789/10489