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'Triangular Hexagons' printed from https://nrich.maths.org/
Well these are things that some of the children have found out and they've been put together for ease of exploring.
Using Equilateral Triangles that are two units along each side - 3 dots for each side.
| Dots |
|
|
Lines |
|
Triangles |
| Around |
Inside |
Total |
Unit length |
Others |
|
| 1/12 |
7 |
19 |
12 |
9 |
6 |
| 2/24 |
37 |
61 |
42 |
15 |
24 |
| 3/36 |
91 |
127 |
120 |
21 |
54 |
| 4/48 |
169 |
217 |
156 |
27 |
96 |
Well if you look at these sequences and explore them there's certainly a lot going on.
Then there are the patterns for equilateral triangles of 1 unit length sides.
One group of children were exploring the number of dots used in each successive size of hexagon and got: 1st 7
2nd 19
3rd 37
4th 61
5th 91
6th 127
They noticed that they are . . . . all PRIME !!!
Then one noticed that they were all related by taking one away and dividing by the order number. So 7 minus 1 divided by 1 is 6 And 19 minus 1 divided by 2 is 9 etc. and he got the sequence
6 9 12 15 18 21