Triangular numbers {1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ... } can be represented geometrically by building equilateral triangles with increasing rows.

Figurate number problem scenarios

The Pythagoreans held the triangular number 10 in the highest esteem, considering it of supreme mystical significance. Its name, the tetraktys, meant literally “the holy four-foldness”, representing the four elements: fire, water, air, and earth (Gullberg, 1997, 289).

ACTIVITY: explore Gauss' trick