A European Square Root Algorithm
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ABCDEFGHIJKLMNOPQRSTUVWXYZ
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This spreadsheet illustrates a method for finding square roots from Europe in the Middle Ages.
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Call the number whose square root you want N.
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Across the top row, start with 1. Skip a space, then multiply by N.
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Repeat for as long as you want.
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Fill in guesses in the blank spaces. You can just repeat the previous number.
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In the next row, add the two numbers in the row above (as in Pascal's Triangle).
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When the row is only two numbers long, take the ratio. This is (approximately) the square root of N.
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Change only the numbers in shaded cells. You only really need to enter N in cell C13.
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It produces two numbers whose ratio approaches
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Find the square root of this number:
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ratio of 1st 2 terms
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11155252512512562562531253125156251562578125
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326103050150250750125037506250187503125093750
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28164080200400100020005000100002500050000125000
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2.333333333245612028060014003000700015000350007500017500000
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2.28017640088020004400100002200050000110000250000000
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2.25256576128028806400144003200072000160000360000000
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2.23076923183218564160928020800464001040002320005200000000
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2.2380952382688601613440300806720015040033600075200000000
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2.23529411887041945643520972802176004864001088000000000
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2.23636363628160629761408003148807040001574400000000
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2.2359550569113620377645568010188802278400000000
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2.23611111129491265945614745603297280000000
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2.23605150295436821340164771840000000
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2.23607427130883846905856
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For comparison, the spreadsheet's calculation of the square root of
5is 2.236067977
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