Triangular Numbers

Date: 4/11/96 at 10:37:41
From: Anonymous
Subject: Triangular Numbers

What is a Triangular Number?

I have tried to look it up in my brother's math book, but 
it's not there! I even tried my own math book too! 

Date: 4/14/96 at 1:13:58
From: Doctor John
Subject: Re: Triangular Numbers

Triangular numbers are the number of dots you need to make 
triangles.These are the first few triangular numbers.

    *        *          *            *             *
            * *        * *          * *           * *
                      * * *        * * *         * * *
                                  * * * *       * * * *
                                               * * * * *
    1        3          6            10           15

The way to get these numbers without drawing pictures is to add up
all the numbers that come before a certain number.  For example,
the tenth triangular number is 1+2+3+4+5+6+7+8+9+10.  Another way 
to get the nth triangular number (n is any number bigger than 
zero) is to multiply n by one more than n and then divide by 2.  
This comes out exactly the same.  By this method, the tenth 
triangular number is 10*11/2 = 55.

-Doctor John, The Math Forum