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Sebastian
Joined: 11 May 2014 Posts: 41 Location: Germany

Posted: Wed Jul 07, 2021 6:07 pm Post subject: Square Roots 


Hello Curta fans,
I would like to know which approximation method you use to calculate square roots, or which one you know? _________________ Type I
5023
8121
11140
22146
22961
22983
26713
66561
80151
Type II
500438
502852
507157
509135
555001
555476 

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murff
Joined: 27 Oct 2009 Posts: 592 Location: Switzerland

Posted: Wed Jul 07, 2021 6:56 pm Post subject: 


... To be honest  I have once according to this instruction (Quadratwurzel nach Toepler) the example recalculated. Also in the Curta Handbook by Bernard Stabile there is a solution for square roots... But would certainly not be able to calculate a square root without instructions!
Maybe I should practice a little _________________ :: m u r f f
:: curta.li 

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Sebastian
Joined: 11 May 2014 Posts: 41 Location: Germany


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murff
Joined: 27 Oct 2009 Posts: 592 Location: Switzerland

Posted: Sat Jul 10, 2021 7:35 pm Post subject: 


OK  I will try!
Let's turn the numbers...
_________________ :: m u r f f
:: curta.li 

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dakota
Joined: 31 Aug 2023 Posts: 4 Location: Mesa, AZ USA

Posted: Sun Sep 10, 2023 12:14 am Post subject: 


I can't read German too well, but I have that PDF now. I want to learn this. I think I know but can you translate the paragraphs below the formula [5]? Or write up a set of operations for this. It looks fascinating!! 

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Pete42
Joined: 23 Sep 2022 Posts: 28

Posted: Sun Sep 10, 2023 8:22 am Post subject: 


dakota wrote: 
I can't read German too well, but I have that PDF now. I want to learn this. I think I know but can you translate the paragraphs below the formula [5]?

The general idea behind the modification of the Toepler algorithm is to multiply the radicand by 5 before applying a modified Toepler algorithm with consecutive subtraction of 5, 15, 25, ... instead of 1, 3, 5, ...
This gives exactly the same result, but the entry of the numbers to subtract is much easier because you only have to change the slider for the tens digit, while the one for the units remains fixed at 5.
Translation of the relevant part (slightly edited automatic translation by deepl.com):
Quote:  Further automation of the process is achieved due to the simple fact that
(formula)
holds. Thus, if the radicand is multiplied by 5 in advance, the algorithm can be applied by successively subtracting five times the odd numbers, i.e. the sequence 5, 15, 25, .... . The rest of the procedure remains unchanged.
This makes the adjustments to be made by the operator much simpler and ultimately allowed automatic processing on electromechanical devices. For example, it is no longer necessary to carry forward (change the tens digit) from 9 to 11 or 19 to 21, etc., but only to move the lever with the tens digit of the sequence 5, 15, 25, 35, ... in each case by one place. Carl Friden used this property to design his electromechanically operating automatic root machines, which came onto the market in 1952 and could automatically draw roots from numbers with up to ten digits.

Generally, deepl.com gives extremely good translation results for the languages it supports, much better than what Google Translater ever achieved (and without Google's privacy issues). I highly recommend it. 

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dakota
Joined: 31 Aug 2023 Posts: 4 Location: Mesa, AZ USA

Posted: Sun Sep 10, 2023 4:16 pm Post subject: 


Thank you so much! I'll give this a try (I'm a bit thick headed because I don't even know Toepler's Method in the first place . 

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dakota
Joined: 31 Aug 2023 Posts: 4 Location: Mesa, AZ USA

Posted: Sun Sep 10, 2023 7:02 pm Post subject: 


And some more searching turned up this document describing Friden's method
How the Friden Extracted Square Roots
as hinted in your translation for me. Thanks again!!! 

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