Triangular Numbers

The name 'Triangular Number' is given to any number in the series ~

1~3~6~10~15~21~28~36~ and so on

If you do not spot a pattern in that list then spend a moment thinking about the difference between the first and second numbers on the list ~ and then the difference between the second and the third ~ and ~ and ~

Visualization of some triangular numbers explains almost everything you will need to know. This pattern ~ below ~ illustrates the triangular number 10.

Triangular numbers illustrated by coins
Triangular numbers are the totals of the number of ~
coins as this pattern repeats to the right ~
The pattern continues ~
for ever ~ by adding one extra coin to ~
the quantity used of the previous row

There are fifteen red balls on a snooker table ~ 15 is the next triangular number following on from 10.

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Last updated 2021~0131... of file