The Relationship Between Triangular and Square Numbers

Triangular number in mathematics are the kind of numbers that would represent a right-angled triangle in the following fashion. You can click the link below and take a look at the triangle.

Click to see the Triangular Number Image

As you can see, there’s a triangle with a base and on top of the base, you have rows made of some number of marbles let’s say, and the next row, again made of marbles but as you move up in the triangle across the rows, the number of marbles is reduced by one each time you move up one row. The triangle is complete when you reach a row with just one marble.

So in this way, we can list the following triangular numbers: 1, 3, 6 , 10, 15, …

It turn out that you can add any two consecutive triangular numbers and get a square number. Let’s look at an image to see how it can be done:

Click to see how to add triangular numbers to get square numbers

So what this means is that, you can add any two consecutive triangular numbers to get a perfect square. We’ll most probably use this result later.

Author: Gahara Raschedian

Math and Science Teacher

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