Conversation

The size of an A4 sheet of paper is 210mm × 297mm. 297/210 = 1.4142 This is a special number. Let' see: A3 is 297×420. 210/148=1.414 A2 is 420×594. 594/420=1.4142 This true all the way up to A0: 841×1189. 1189/841=1.414 Can you guess why? (Answer in next tweet)
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1.414 is of course √2. Why do all these paper sizes have a ratio of 1:√2? Because this ensures that if you cut an A0 into two pieces, you get an A1. And A1 halved gives A2. And A2 begets A3. And fold A3 into two to get A4.
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But why is A0 841mm×1189mm? Let's try multiplying instead of dividing: 841×1189 = 1009461. The reason it is suspiciously close to one million is because it was intentional: the size A0 was chosen to give a paper of 1 square meter (but rounding to the closest mm)
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Coda: Technical pens (i.e. the ones used by engineers, architects, drafters) come in these sizes: 0.10, 0.13, 0.18, 0.25, 0.35, 0.50, 0.70, 1.0, 1.4, and 2.0mm. Notice anything? 2.0/1.4 ≈ 1.4/1.0 ≈ 1.0/0.7 ≈ ... ≈ √2 Why do the sizes have similar ratios to paper sizes?
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