Why are 1, 3, 6, 10, 15, … called triangular numbers? Why are 1, 4, 9, 16, 25, … called square numbers or squares? Why are 1, 8, 27, 64, 125, … called cubes?

Triangular numbers (1, 3, 6, 10, 15, …) are called so because they can be represented by dots arranged in the shape of a triangle. For example, 3 dots form a triangle with two at the bottom and one at the top. Square numbers (1, 4, 9, 16, 25, …) are called squares because they can be arranged in a square grid, like 4 dots forming a 2 x 2 square. Cubes (1, 8, 27, 64, 125, …) represent the number of small cubes that fit into a larger cube, with each number being the cube of an integer, like 3 x 3 x 3 for 27.