Geodesic
Two hidden properties of hex numbers
The Teaching of Mathematics, XXV (2022) no. 1, p. 21 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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In this paper, we prove that the $n$-th hex number is exactly the sum of the number of pieces and the number of triple points associated with an `$n$-balanced' partition of a triangle obtained by $n-1$ cevians from each vertex. Moreover, we see via hex numbers an extension of a Feynman's result: the $(k+1)$-th hex number is the ratio of the area of a triangle $T$ and the area of central triangle associated with a regular partition of $T$ of order $2k+1$.
Classification : 97G30, G34
Keywords: hex numbers, cevians, balanced partitions of triangles, regular partitions of triangles, Feynman's triangle. 
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     author = {Silvano Rossetto and Giovanni Vincenzi},
     title = {Two hidden properties of hex numbers},
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Silvano Rossetto; Giovanni Vincenzi. Two hidden properties of hex numbers. The Teaching of Mathematics, XXV (2022) no. 1, p. 21 . http://geodesic.mathdoc.fr/item/TM2_2022_XXV_1_a2/