Talk:Trachtenberg system

Incoherent
Much of this is rather incoherent. In particular the meaning of "neighbor" is very confusing. -- Jmabel 05:58, Aug 7, 2004 (UTC)

Link removed
removed the link *http://www.speed-math.com/. Little relevance to the article.

I disagree about the irrelevance of the link: it is clearly software for practicing Trachtenburg method as described in the book.18.209.1.147 08:03, 29 December 2006 (UTC)

Here is one clearer examples
I rewrote the demonstration of multiplication by 12. I hope it is clearer. It could still use work.

without paper.
I removed the phrase 'without pencil and paper'. I don't believe such a claim is made for the trachtenberg system. The system allows one to work quickly, even for large numbers. I will double check this, but I feel sure enough to make the edit for now.

needs work
as previously mentioned I did a quick and clumsy rewrite of one of the examples. but the whole article needs work. The examples may make sense to someone familiar with the trachtenberg system but others would be confused. enhandle


 * I added a brief explanation as to what halving meant, and how it's supposed to speed things up. But it really could use a treatment of how to add, multiply, and square things quickly. --Eienmaru 08:00, 16 May 2005 (UTC)

Mental Arithmetic
I have now checked the book on the Trachtenberg system. There is no claim or intent to be a mental, paperless methodology. Perhaps some use it that way. but the examples given use very large numbers and explanations of pencil work. It would be near impossible for any ordinary person to do these things in his head.

I also am now forced to wonder at the comparison to Vedic. perhaps. perhaps not. I do not have the time or inclination to research it.


 * I agree. I used to be able to do up to about 3 x 3-digit multiplication without a pencil, but anything higher and the digit stacks get too long for me to remember.  There are only so many registers in the human brain, after all ^_^ --Eienmaru 08:00, 16 May 2005 (UTC)


 * Not really. By solving the problem in columns instead of rows as we were taught you can add up the numbers immediately upon finding them.  I've been doing 4x4 and 5x5 digit multiplication in my head with this system.  As I find each number, I add it in to the running total in my head.  There are no saving numbers for later use.  Trachtenberg did develop this method in a concentration camp without the benefit of paper or pencil.  Of course, I do have to write down each digit of the answer as I find it.  Perhaps that is what you meant. Netherstar (talk) 23:34, 6 February 2011 (UTC)

this is very confused
This article is very confused. I don't have time to clean it up right now, but whoever does should have a look at http://hucellbiol.mdc-berlin.de/~mp01mg/oldweb/1mutrach.htm. (The french article isn't any better.)
 * you always have to add a 0 at the left, one for each digit of the multiplier
 * neighbour always means to the right
 * you work from right to left
 * you carry the one
 * Finally, the bulk of the article covers on multiplication, and only partially, even though the actual system also includes addition, division, and other special case stuff like certain squares. It seems odd to include so much detail about certain multiplicative cases when the others are left out.

Indeed. The following is moved from Translation into English:


 * Article: fr:Méthode Trachtenberg
 * Corresponding English-language article: Trachtenberg system
 * Worth doing because: Material to incorporate into English-language article
 * Originally Requested by: 80.160.122.64 00:43, 29 May 2004 (UTC)
 * Status: completed by --Frenchgeek 05:12, Aug 7, 2004 (UTC)
 * Other notes: One of the external links is to a website that advertises a product. Should I delete that link?
 * Not really a translation issue, can be dealt with in the usual manner -- Jmabel 21:44, Sep 16, 2004 (UTC)
 * The word translated here as "neighbor" is unclear in its meaning. Can someone nail that before I remove this and call it complete? -- Jmabel 21:44, Sep 16, 2004 (UTC)
 * using neighbour for voisin is fine. It's good.
 * It isn't good because it is never defined in the relevant context. What does it mean? Digit to the left? Digit to the right? Both? Something else?
 * this is not a translation problem IMO. The french and english articles are equally ambiguous. I have studied math in both fr. and eng. and voisin / neighbour do not have any special meaning. I would suggest that study of the method, not the french text, is needed to discover the accurate method.

Two-finger Method
The "crown jewel" of the Trachtenburg system is a rapid method of multiplication of two numbers each of arbitrary number of digits. It is called the "two finger method", and this article ought to have a description of it.

Book
Could someone find the year of publication for the book? Larry R. Holmgren 17:29, 15 July 2007 (UTC)

I recorded on the page for Jakow Trachtenberg the year 1965 for its publication in London by Pan Books, per the copy of this book in my possession. Dajwilkinson 23:40, 15 July 2007 (UTC)

Trachtenberg X 12 multiplication.
When you perform a multiplication first write down the number to be multiplied on paper and then perform the calculation from right to left.

Let's say 12345 x 12

First put zeros in front, 2 this time as we are multiplying by a 2 digit number. At each step mark the number you are dealing with. First Step * 0012345

The 'neighbour is the one to the right of the 5 ... NO Neighbour. So just double the number and the result goes below the marked number. * 0012345      0 the result being  10 you have to carry the 1 to be added in  the next step. ** 0012345      0 The second step, mark above the 4 and we now have a neighbour to the right, the 5. Double the number, add in the neighbour and the carry 8 + 5 + 1 = 14 0012345     40 Once again remember the carry one. This process is continued until you reach the zero when you add in the neighbour only. In this case the 1 and there is no carry. ** 0012345 148140

Hope this helps convert someone to a brilliant way of doing arithmetic ......

Modified the article to avoid any copyright problems.--PeterDKnight 11:35, 16 September 2007 (UTC)

Multiplying by 5
This section is uselessly unreadable. Ugh. What a waste of server space. 128.151.178.66 (talk) —Preceding undated comment was added at 21:06, 5 February 2009 (UTC).

I agree. Multiply x 5???? >>>> add a zero and divide by 2. Not Trachtenberg but it works ;-) 195.217.128.34 (talk) 13:53, 4 February 2010 (UTC)

Plan to streamline
I've recently learned this system and I've found it very interesting. However, this article contains several points of misinformation and confusion caused by differences from different contributors. I've already changed the topic for Multiplying by 5 and intend to make some other changes in the future. I may completely rewrite the article. I haven't decided yet. If this causes problems for anyone, please let me know. Netherstar (talk) 21:55, 31 December 2010 (UTC)


 * I've started a rewrite on this article, but I've been informed that an entire rewrite is not advisable without a discussion on this talk page. The rewrite can be found here.  I had all the rules for 3 thru 12 but I commented out several of them.  I began to feel that it was too much information.  This is an enclyclopedia, not a training seminar.  I also improved the cohesion between sections and corrected the citations.  Please let me know what anyone thinks.  Netherstar (talk) 00:20, 4 January 2011 (UTC)

Reorder of the rules
I have rearranged the order of the simple number rules because there is a pattern to the rules that the book never explains.

And rule 5 is it's own animal and falls outside any pattern.

Addendum #1: If the rule states to add half the neighbor, always drop any 0.5 you get. Addendum #2: If the rule states to add half the neighbor, always add five if the current digit is odd.

Actually, rule 2 exists because of rule 1. You add five when the current digit is odd in anticipation of dropping the 0.5 in the next digit. Example: 632 --> 0.5 Hundreds = 5 Tens.

But because all of this is not in the book it falls under the catagory of "original research" and can not be included in the main article.

Netherstar (talk) 17:30, 5 February 2011 (UTC)

Non-mathematicians point of view
I'm not that good at maths but I was wondering if it would be better if the article started with the x12 method. I didn't have a clue about the lengthy opening paragraphs about the algorithms but as soon as I saw the example given for x12 it took me five minutes to work out (as in understanding what the example was illustrating). I always think that simple examples are far better for non-mathematicians. It would be great for readers if there was an early heading: A simple example of the multiplication method using x12

Sluffs (talk) 22:58, 3 November 2013 (UTC)

How about these examples:

Find the product of 111 x 12. Add a zero to the start of the multiplicand (the number that is to be multiplied) so 01111. Start from the right and double each figure and add the right neighbor. The first figure has no neighbor and therefore receives no addition. Note that the prefix zero has to be calculated (double 0 then add the neighbor).

Find the product of 444 x 12. When a step produces ten or above carry the one.

Sluffs (talk) 00:27, 4 November 2013 (UTC)

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Better Algorithm
The C++ example is overly complicated. Instead of all the added complexity of classes and OOP, the example (which I agree should be there) should be more like pseudo-code. At the very least, it should be procedural and not object-oriented. Ackbeet (talk) 17:19, 18 April 2019 (UTC)

pedido de tradução
por traduzam este artigo Lil dripp (talk) 23:45, 10 October 2023 (UTC)

Plagiarism at https://artofmemory.com/wiki/Trachtenberg_System/
Why does this keep happening? It's super obvious to people who are researching the subject and already checked the Wikipedia article. 63.155.46.234 (talk) 05:17, 30 April 2024 (UTC)