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

Question

Bright Tutorials · Accepted Answer

(a) Triangular numbers are called so because these numbers of dots can be arranged to make a triangle.
1, 3, 6, 10,…….. are triangular numbers.
1, 3, 6, 10,……… dots can be arranged to make a triangle. (see figure below)
(b) Square numbers are called so because these numbers of dots can be arranged to make a square.
1, 4, 9, 16,………. are square numbers.
1, 4, 9, 16,……… dots can be arranged to make a square (see fig. below)
(c) Cubes are called so because these many unit cubes can be arranged to make a cube.
1, 8, 27, 64,…… are cube numbers.
1, 8, 27, 64,……. unit cubes can be arranged to make cubes. (see figure below)

Patterns in Mathematics — Question 6