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I often have to generate triangle numbers so I created this simple online utility that does it for me. It lets you generate however many triangular numbers you need starting from any position or value. It works in the browser and is powered by alien technology from the future.

## Triangle Number Generator Options

## Triangle Number Generator Examples (click to try!)

_{100}. The 100th number is calculated via the expression 100(100+1)/2 and is equal to 5050, the 101st number is calculated via 101(101+1)/2 = 5151, and so on. All computed numbers are separated by the comma symbol.

5050, 5151, 5253, 5356, 5460, 5565, 5671, 5778, 5886, 5995, 6105, 6216, 6328, 6441, 6555, 6670, 6786, 6903, 7021, 7140, 7260, 7381, 7503, 7626, 7750, 7875, 8001, 8128, 8256, 8385, 8515, 8646, 8778, 8911, 9045, 9180, 9316, 9453, 9591, 9730, 9870, 10011, 10153, 10296, 10440, 10585, 10731, 10878, 11026, 11175

_{6×6}= 666. To print this list, it uses the "Start from a Value" generator mode and specifies 666 below it. All numbers are printed on separate lines.

666 703 741 780 820 861 903 946 990 1035

^{2}).

1bc16d678a62ca00 1bc16d6801985e01 1bc16d6878cdf203 1bc16d68f0038606 1bc16d6967391a0a

## How Does This Triangle Number Generator Work?

This triangle number generator works entirely in your browser and is written in JavaScript. It can calculate triangular integers starting from any position or any value. It uses the mathematical formula `T(n) = n(n+1)/2`

to find the n-th triangle number. If the starting value is given, then it inverts the formula by first multiplying both sides by two `2T(n) = n(n+1)`

, then expanding the `n(n+1)`

term to `2T(n) = n`

, and then bringing all terms to one side ^{2} + n`n`

. The solution to this quadratic equation gives us the starting index ^{2} + n - 2T(n) = 0`n = (sqrt(1+8x) - 1)/2`

. To find `count`

(specified in options) numbers, it uses a loop from `1`

to `n`

and at every iteration computes `T(n)`

. All `T(n)`

values are converted to the given base (specified in options) and are saved for output in a variable `tNumbers`

. As the triangle numbers grow quickly, this tool uses the `bignumber.js`

library to support arbitrary large computations. When the output variable `tNumbers`

is printed, the values are combined together and the separator symbol is placed between them. The separator symbol can be set in the options.

### Created by Browserling

This triangle number generator was created by me and my team at Browserling. Behind the scenes, it's actually powered by our web developer tools that are used by millions of people every month. Browserling itself is an online cross-browser testing service powered by alien technology. Check it out!

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