Johnson, Virginia P.; Cook, Charles K. Areas of triangles and other polygons with vertices from various sequences. (English) Zbl 1401.11038 Fibonacci Q. 55, No. 5, 86-95 (2017). Summary: Motivated by Elementary Problems B-1167 [O. Liba and A. Shurki, ibid. 53, No. 2, 180–185 (2015), https://www.fq.math.ca/53-2.html] and B-1172 [S. Edwards, ibid. 53, No. 3, 272–278 (2015), https://www.fq.math.ca/53-3.html], formulas for the areas of triangles and other polygons having vertices with coordinates taken from various sequences of integers are obtained. Cited in 2 Documents MSC: 11B39 Fibonacci and Lucas numbers and polynomials and generalizations 51M04 Elementary problems in Euclidean geometries PDFBibTeX XMLCite \textit{V. P. Johnson} and \textit{C. K. Cook}, Fibonacci Q. 55, No. 5, 86--95 (2017; Zbl 1401.11038) Full Text: arXiv Link Online Encyclopedia of Integer Sequences: Tetrahedral (or triangular pyramidal) numbers: a(n) = C(n+2,3) = n*(n+1)*(n+2)/6. Padovan sequence (or Padovan numbers): a(n) = a(n-2) + a(n-3) with a(0) = 1, a(1) = a(2) = 0. Areas of triangles associated with tribonacci sequence. Areas of triangles associated with the Padovan sequence. Twice the area of triangle with coordinates (Fn, Fn+k), (Fn+2k, Fn+3k) and (Fn+4k, Fn+5k), where Fn is the n-th Fibonacci number A000045.