Areas of polygons with vertices from Lucas sequences on a plane
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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.
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.
참고문헌 (9)
- S. Edwards, "Elementary problems and solutions B–1172", Fibonacci Quart, 53, pp.180~181 (2015)
- H. Harborth, "Fibonacci triangles, in Applications of Fibonacci numbers, Vol. 3", pp.129~132 (1990), Kluwer Acad. Publ
- H. Harborth, "Non-existence of Fibonacci triangles", Congr. Numer, 114, pp.29~31 (1996)
- P. Johnson, "Elementary problems and solutions B-1172", Fibonacci Quart, 54, pp.273~275 (2016)
- V. P. Johnson, "Areas of triangles and other polygons with vertices from various sequences", Fibonacci Quart, 55(5), pp.86~95 (2017)
- H. Kwong, "Elementary problems and solutions B–1167", Fibonacci Quart, 54, pp.180~181 (2016)
- S. Lipschutz, "Schaum’s outline of Discrete Mathematics" (2007), McGRAW–HILL
- "Shoelace formula"[URL]
- A. Shriki, "Elementary problems and solutions B–1167", Fibonacci Quart, 53, pp.179~ (2015)