International Journal of Research Studies in Education
Special Luminary Issue
2025
Volume 14 Issue 4
Available Online: 20 February 2025
Author/s:
Tabirara, Yorihc*
Manila Science High School, Philippines (tabirarayorihc@gmail.com)
Pineda, Charlemaigne
Manila Science High School, Philippines (charlemaignepineda0430@gmail.com)
Dela Cruz, Johne Noel
Manila Science High School, Philippines (johnenoeldelacruz@gmail.com)
Abstract:
The Method of Moving Points is a type of transformation revolving around projective geometry. This method has been utilized to prove certain congruences in lines and circles. Through the use of this concept, two objects belonging to a projective map are essentially invariant or transformations of each other regardless of end behavior when given the conditions of bijectivity and similarity of cross-sections, which apply in fixed points. Invariance typically applies when distinct points that lie on a complex plane yield a cross-ratio that is preserved and well-defined. Building upon this foundation, we aim to explore the concept of moving points in complex curves, particularly in ellipses. In cases of untethered moving points, such as those of ellipses, concepts of degree bounds introduced by Zack’s lemma take part in determining the number of cases to be proven by Lagrange interpolation. This paper seeks to provide an extensive application of the method of moving points in ellipses and proving special cases through geometric concepts.
Keywords: projective map, conics, cross-ratio, untethered points, Zack’s lemma, Lagrange interpolation
DOI: https://doi.org/10.5861/ijrse.2025.25842
Cite this article:
Tabirara, Y., Pineda, C., & Dela Cruz, J. N. (2025). Geometric characterizations of the method of moving points in ellipses. International Journal of Research Studies in Education, 14(4), 137-153. https://doi.org/10.5861/ijrse.2025.25842
* Corresponding Author