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Magic square
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===A method for constructing a magic square of order 3=== In the 19th century, [[Édouard Lucas]] devised the general formula for order 3 magic squares. Consider the following table made up of positive integers ''a'', ''b'' and ''c'': {| class="wikitable" style="margin-left:auto;margin-right:auto;text-align:center;width:26em;height:6em;table-layout:fixed;" |- | ''c'' − ''b'' || ''c'' + (''a'' + ''b'') || ''c'' − ''a'' |- | ''c'' − (''a'' − ''b'') || ''c'' || ''c'' + (''a'' − ''b'') |- | ''c'' + ''a'' || ''c'' − (''a'' + ''b'') || ''c'' + ''b'' |} These nine numbers will be distinct positive integers forming a magic square with the magic constant 3''c'' so long as 0 < ''a'' < ''b'' < ''c'' − ''a'' and ''b'' ≠ 2''a''. Moreover, every 3×3 magic square of distinct positive integers is of this form. In 1997 [[Lee Sallows]] discovered that leaving aside rotations and reflections, then every distinct [[parallelogram]] drawn on the [[Argand diagram]] defines a unique 3×3 magic square, and vice versa, a result that had never previously been noted.<ref name=lost-theorem/>
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