Sticky triangles
1 I made a triangle of 4 layers of triangles.
2 I recorded some data including:
- number of match sticks in my 4 layer triangle
- the upright triangles
- the upside down triangles
- the total number of triangles.
I repeated this process on a 3 layer triangle a 2 and a 1
3 I looked for patterns such as the total triangles are triangular numbers but the most important pattern for working out the formula was that the number of match sticks was 3 times more than the number of upright triangles.
4 This led me to creating an expression n= number of layers, or if you were to lay the triangles out in height order, it would be the nth term of that sequence.
The expression looked like this.
3 (n(n+1))= number of sticks please note: The external 3 vertical brackets
(______) should be one vertical bracket!
( 2 ) I can't show it on the computer!
( 2 )