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Two diagrams in burgundy, blue and gold on soft rose: a square with four rectangles along its sides, labelled x² and 2½x, and the same figure completed into a larger square by four small corner squares of 6¼, with the equations beneath.
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The Pattern Atlas

Completing the Square

No. 40 of 100 · free · 300 dpi

What you seeTwo diagrams in burgundy, blue and gold on soft rose: a square with four rectangles along its sides, labelled x² and 2½x, and the same figure completed into a larger square by four small corner squares of 6¼, with the equations beneath.

What it meansIn his treatise on al-jabr, written in Baghdad in the ninth century, al-Khwarizmi solved equations with words and figures. For a square and ten roots equal to thirty-nine he added four squares of six and a quarter to make sixty-four, a square of side eight, so the root is three.

Where it worksA clever plate for a study, a classroom or anyone who loves mathematics.

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2:3 · 7200 × 10800 px4×6 · 8×12 · 12×18 · 16×24 · 20×30 · 24×36 in
3:4 · 5400 × 7200 px6×8 · 9×12 · 12×16 · 18×24 in
4:5 · 7200 × 9000 px4×5 · 8×10 · 16×20 · 24×30 in
11:14 · 3300 × 4200 px11×14 in
A-series · 7023 × 9933 pxA5 · A4 · A3 · A2 · A1

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