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The product of a number multiplied by itself, e.g. 1, 4, 9, 16.
‘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.’
‘Since the next succeeding square number is 729, which has 27 for its side, divide 720 by 27.’
‘This year I've decided to switch my mathematical allegiance to square numbers.’
‘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.’
‘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.’