There are unexpected discoveries to be made about square numbers…
You’re probably very familiar with the sequence of Square Numbers:
Below are some ideas to explore with square numbers.
For each one, try a few examples and see what you notice.
- Add two consecutive square numbers and then subtract 1
- Square any odd number, then subtract 1
- Multiply two consecutive odd numbers and then add 1
- Multiply two consecutive even numbers and then add 1
Can you explain what you’ve noticed?
Can you prove that it will always happen?
Can you come up with any Square Number Surprises of your own?
Age 14 to 16