Abstract

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 $2k+1$.

Keywords: Hex numbers; cevians; balanced partitions of triangles; regular partitions of triangles; Feynman's triangle.

Pages:  21$-$29     

Volume  XXV ,  Issue  1 ,  2022