Morgan's theorem is a generalization of Marion's theorem found by Ryan Morgan, a sophomore at Patapsco High School in Baltimore (Morgan 1994).
If the sides of a triangle are partitioned into equal segments for an odd integer and each
division point is connected to the opposite vertex, a central hexagon
is formed. Morgan's theorem states that the area of this
hexagon relative to the original triangle
is
(Morgan 1994, Watanabe et al. 1996). For , 5, 7, ..., this gives one over the centered nonagonal numbers
10, 28, 55, 91, 136, 190, 253, 325, 406, ... (OEIS A060544).
equal segments for 
an odd integer and each
division point is connected to the opposite vertex, a central hexagon
is formed. Morgan's theorem states that the area of this
hexagon relative to the original triangle
is
, 5, 7, ..., this gives one over the centered nonagonal numbers
10, 28, 55, 91, 136, 190, 253, 325, 406, ... (OEIS A060544).
