Geodesic
Two hidden properties of hex numbers
The Teaching of Mathematics, XXV (2022) no. 1, p. 21

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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. 
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/
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