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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
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
Sebastian

Joined: 11 May 2014
Posts: 41
Location: Germany

 Posted: Thu Jul 08, 2021 4:12 pm    Post subject: Thanks murff. Some time ago I discovered another (easier) way to calculate square roots - unfortunately I don't know where I found this approximation method. https://docplayer.org/32458491-Zur-berechnung-von-quadratwurzeln-mittels-mechanischer-rechenmaschinen-detlef-kraus.html Formula [5] on page 4 is the one I'm using - it's easy and you don't need any aproximat value or anything else._________________Type I 5023 8121 11140 22146 22961 22983 26713 66561 80151 Type II 500438 502852 507157 509135 555001 555476
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
dakota

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

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

 Sebastian wrote: Thanks murff. Some time ago I discovered another (easier) way to calculate square roots - unfortunately I don't know where I found this approximation method. https://docplayer.org/32458491-Zur-berechnung-von-quadratwurzeln-mittels-mechanischer-rechenmaschinen-detlef-kraus.html Formula [5] on page 4 is the one I'm using - it's easy and you don't need any aproximat value or anything else.

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!!
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.
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 .
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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