Definition:Fleenor-Heronian Triangle

Definition

A Fleenor-Heronian triangle is a Heronian triangle whose sides have lengths form a set of $3$ consecutive integers.

Sequence of Fleenor-Heronian Triangles

The sequence of Fleenor-Heronian triangles begins:

$\paren {1, 2, 3}$

$\paren {3, 4, 5}$

$\paren {13, 14, 15}$

$\paren {51, 52, 53}$

$\paren {193, 194, 195}$

$\paren {723, 724, 725}$

$\paren {2701, 2702, 2703}$

$\paren {10 \, 083, 10 \, 084, 10 \, 085}$

$\paren {37 \, 633, 37 \, 634, 37 \, 635}$

Also see

• Definition:Heronian Triangle

Source of Name

This entry was named for Charles R. Fleenor and Heron of Alexandria.

Sources

• 1996-7: Charles R. Fleenor: Heronian Triangles with Consecutive Integer Sides (J. Recr. Math. Vol. 28, no. 2: pp. 113 – 115)