Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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AREAS OF POLYGONS WITH VERTICES FROM LUCAS SEQUENCES ON A PLANE

  • Received : 2022.08.19
  • Accepted : 2022.12.23
  • Published : 2023.07.31
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Abstract

Area problems for triangles and polygons whose vertices have Fibonacci numbers on a plane were presented by A. Shriki, O. Liba, and S. Edwards et al. In 2017, V. P. Johnson and C. K. Cook addressed problems of the areas of triangles and polygons whose vertices have various sequences. This paper examines the conditions of triangles and polygons whose vertices have Lucas sequences and presents a formula for their areas.

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Acknowledgement

We would like to thank the referees for valuable comments that help to improve our manuscript.

References

  1. S. Edwards, Elementary problems and solutions B-1172, Fibonacci Quart. 53 (2015), 180-181. https://doi.org/10.1080/00150517.2015.12428281
  2. H. Harborth and A. Kemnitz, Fibonacci triangles, in Applications of Fibonacci numbers, Vol. 3 (Pisa, 1988), 129-132, Kluwer Acad. Publ., Dordrecht, 1990.
  3. H. Harborth, A. Kemnitz, and N. Robbins, Non-existence of Fibonacci triangles, Congr. Numer. 114 (1996), 29-31.
  4. P. Johnson, Elementary problems and solutions B-1172, Fibonacci Quart. 54 (2016), 273-275.
  5. V. P. Johnson and C. K. Cook, Areas of triangles and other polygons with vertices from various sequences, Fibonacci Quart. 55 (2017), no. 5, 86-95.
  6. H. Kwong, Elementary problems and solutions B-1167, Fibonacci Quart. 54 (2016), 180-181. https://doi.org/10.1080/00150517.2016.12427795
  7. S. Lipschutz and M. Lipson, Schaum's outline of Discrete Mathematics, Third Edition, McGRAW-HILL, 2007.
  8. Shoelace formula, Wikipedia, https://en.wikipedia.org/wiki/Shoelace_formula, 2022.
  9. A. Shriki and O. Liba, Elementary problems and solutions B-1167, Fibonacci Quart. 53 (2015), 179.