Isosceles Triangle Numbers

9 is an isosceles triangle number
9 is an isosceles triangle number
16 is a square number
16 is a square number
The next person produced this answer, which means the number 16 went on the Isosceles Triangle list as well.
16 is an isosceles triangle number

A bit more experimentation, and we realised a couple of things – it was easy to play around with this investigation on 1cm squared paper, and it let us try find some MUCH bigger isosceles triangle numbers. We also noticed that the bottom row of counters has to contain an ODD number or the triangle won’t come to a point at the top.

We also found some bigger square numbers, and both lists got quite a bit longer.

Then, we noticed something about the lists…. try it. What do you notice? Why??

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