Talk:Trachtenberg system

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

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)

Contents

[edit] Here is one clearer examples

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

[edit] 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.

[edit] 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)

[edit] 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)

[edit] 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 .

  • 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.

(The french article isn't any better.)

Indeed. The following is moved from Wikipedia: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.

[edit] 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.

[edit] 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)


[edit] 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)