Triangular numbers are usually represented as numbers created by organizing rows of dots into equilateral triangles. In other words, if you were drawing triangles that got more prominent by one equal row of beads at a time, you would count the dots that appear inside and outside the triangle. The first digits in the sequence of triangular numbers are 1, 3, 6, 10, and 15.

What is the importance of Triangular Numbers?

Triangular numbers form a pattern and, as such, are a valuable way of getting KS2 and above children to think about algebraic functions and the importance of number formulas. This forms part of a crucial knowledge base for maths students in the future!

Who came up with the Triangular Number theory?

The triangular number formula is widely thought to have originated with the Pythagoreans. They paved the way for other mathematicians by helping to discover the relationship between geometric shapes and numbers.

Meanwhile, Carl Gauss, an 18th-century mathematician, used the formula of triangular numbers to help him calculate the sum of consecutive numbers. He used algorithms at just ten years old to compute the hundredth triangular number!

Triangular Numbers in broader Mathematics

One of the main reasons triangular numbers are essential in mathematics is their close relationship to other number patterns.

For example, square numbers, cube numbers, and other geometric figures follow a similar formula to that used when calculating triangular numbers.

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