The first ten triangular numbers are -

You can calculate triangular numbers by adding up consecutive numbers. For example, the eighth triangular number is equal to -
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8
- which comes to 36.

As the name suggests, you can visualize triangular numbers as a triangle of points.

Everyone in a group of people shakes hands with everyone else. The total number of handshakes will always be a triangular number. For instance, five people will make ten handshakes.

There is a useful short cut if you want to work out a large triangular number. Suppose you want the 100th triangular number. You could add up all the numbers from 1 to 100. But there is a simpler way. First work out the average number by adding together the first and the last number, and dividing by two -
1 + 100 = 101
101 / 2 = 50.5

Now multiply this average by however many numbers you would have to add up, in this case, by 100 -
50.5 x 100 = 5050
- so the 100th triangular number is 5050. 

The first four triangular numbers. How many do you have to add each time?

Here is Patrick De Geest's page about palindromic triangular numbers.

For more facts about numbers get the book Numbers: Facts, Figures and Fiction.

© Copyright Cambridge University Press, University of Nottingham & Richard Phillips 1994/1999. Updated 11 June 1999.  BI666 New Genesis Links Below Home Introduction Contents Discussion Feedback  Back to Ra! Return to What is Ra?   BI666 Math Site Search:   Top of Page