Definition of square number in English:
The product of a number multiplied by itself, e.g. 1, 4, 9, 16.
- If we can express a square number also as the sum of two other square numbers then Pythagoras' Theorem tells us that we have three sides of a right-angled triangle and this is Fibonacci's first Proposition.
- In every right-triangle, if the double product of the legs be either added or subtracted from the square of the hypotenuse, both the sum and the remainder will be square numbers.
- Fibonacci first notes that square numbers can be constructed as sums of odd numbers, essentially describing an inductive construction using the formula n 2 + = 2.