Computing Square Roots by Subtraction on a Walther WSR 160 Mechanical Calculator

Описание: Watch a method for computing square roots by subtraction on a Walther WSR 160 mechanical calculator.

The mathematical background
It seems like a largely forgotten math fact today that all perfect square numbers can be written as the sum of all consecutive odd numbers starting from 1 . For example:

1 + 3 = 4
1 + 3 + 5 = 9
1 + 3 + 5 + 7 = 16
1 + 3 + 5 + 7 + 9 = 25
1 + 3 + 5 + 7 + 9 + 11 = 36
1 + 3 + 5 + 7 + 9 + 11 + 13 = 64
1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 81

etc.

This phenomenon has in fact been known since antiquity, and is the basis for one of the simplest methods to compute square roots: given a specific number N whose root you wish to compute, subtract the numbers from the sequence of odd numbers from N until the remainder is zero. Then the number of subtractions performed is the square root .

A slight problem
Of course, there is a problem, and if you are mathematically inclined, you may have noticed it: The method only works on perfect squares, otherwise a residual remains after all the subtractions have been done.

A simple workaround to this problem is by adding more digits by multiplying the number by 100 or 10,000 etc. before doing the subtractions. But, as the saying goes: every silver lining has a cloud : Adding more digits to the result will require performing more subtractions, as is demonstrated clearly in the clip.

Fortunately, better and more efficient methods for computing square roots exist. In an upcoming clip I'll walk you through the Babylonian Method which is a fast and accurate method you can use if you ever find yourself stranded on a deserted island with only a four-function calculator without square-root capability. Knowledge of such retro-style math tricks might save your day.

Be sure to also check out my other clips of mechanical calculators, including the demonstration of this calculator here:    • Walther WSR 160 Mechanical Calculator | Ho...  

Also check out a clip of the calculator with the covers removed and where you can see the mechanism working:    • Inside Walther WSR 160 Mechanical Calculator  

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