Sticky+Triangles

This puzzle comes from one of my favourite maths websites, @http://nrich.maths.org/

I was exploring a puzzle in which headless match sticks had to be moved to make a different number of triangles. I made one small triangle
 * = [[image:http://nrich.maths.org/content/01/04/bbprob1/onetriangle.gif caption="Triangle from three matches."]] || 3 matches ||

I made it into 4  small triangles by adding 6   matches. I added another row and counted the number of small triangles and counted the matches.   I made a **table** of my results and continued adding rows. I found many patterns. Have a go and see what patterns you can find. You do not have to use sticks - drawing lines will do just as well.
 * = [[image:http://nrich.maths.org/content/01/04/bbprob1/fourtriangles.gif caption="Four triangles."]] || 9 matches ||

Find a good way to record your results (A spreadsheet perhaps?!).

<span style="background-color: #ffffff; font-family: Verdana,tahoma,arial,helvetica,sans-serif; font-size: 18px;">See if you can predict the numbers for rows of triangles you have not drawn.

<span style="background-color: #ffffff; font-family: Verdana,tahoma,arial,helvetica,sans-serif; font-size: 18px;">When you have done all you can with triangles, see if you get the same sort of results with squares. Then think of other shapes which might make number patterns as they grow.