Talk:Ancient Egyptian multiplication

From Wikipedia, the free encyclopedia
Jump to: navigation, search
WikiProject Mathematics (Rated Start-class, Low-importance)
WikiProject Mathematics
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
Start Class
Low Importance
 Field:  Basics (historical)

Name change to Ethiopian Multiplication[edit]

Evidence:, a documentary on the method that refers to this name. --Paddy (talk) 13:14, 29 July 2010 (UTC)

We're descriptivist, not prescriptivist -- that is, we go with what it is most commonly called, not what it should be called. DS (talk) 13:09, 28 August 2010 (UTC)
And that is described where? --Paddy (talk) 15:40, 28 August 2010 (UTC)

Generic name[edit]

This method is also known by its generic name as double-and-add and is related to the square-and-multiply exponentiation. Lauri.pirttiaho (talk) 18:07, 17 September 2011 (UTC)

Inexact formulation[edit]

In the decomposition secion, the sentence "The Egyptians knew empirically that a given power of two would only appear once in a number." makes little mathematical sense. You could rewrite it as "The E. knew empirically that a number had a unique decomposition as sum of powers of two, each power appearing at most once." — Preceding unsigned comment added by (talk) 22:01, 12 December 2014 (UTC)

Background information matches another site[edit]

The Background information section is almost exactly word-for-word from this archived page. As the webpage mentions Wikipedia, it's unclear to me which source is the original text. Paul2520 (talk) 02:01, 19 March 2015 (UTC)

A neat point about this method[edit]

Ancient Egyptian multiplication really shines if you use a base that is a power of two, especially hexadecimal (as has been noted in a post by icarus on the DozensOnline forum, which I can't link to because of the blacklist). This is because it makes repeated multiplication by two cycle after a few steps to the same number with an extra zero at the end, viz.:

  • 1 → 2 → 4 → 8 → 10
  • 3 → 6 → c → 18 → 30
  • 5 → a → 14 → 28 → 50
  • 7 → e → 1c → 38 → 70
  • 9 → 12 → 24 → 48 → 90
  • b → 16 → 2c → 58 → b0
  • d → 1a → 34 → 68 → d0
  • f → 1e → 3c → 78 → f0

You'd of course also have to memorize the binary decomposition of the digits:

Hexadecimal 0 1 2 3 4 5 6 7 8 9 a b c d e f
Binary 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111

I'd prefer saving hexadecimal to octal, because octal is small enough that memorizing the multiplication table is easy, but this may not be the case for hexadecimal. Furthermore, hexadecimal is more symmetrical than octal, as it is 222, unlike octal's non-binary 23. The whole binary mindset seems more consistent in hexadecimal than octal, and so hexadecimal may lend itself better to a thoroughly binary-based algorithm like Ancient Egyptian multiplication.

For example, suppose you want to calculate f6 × 4e. Note that 4e = 40 + 8 + 4 + 2, and then:

 1     f6
 2    1ec
 4    3d8
 8    7b0
10    f60
20   1ec0
40   3d80
4e   4af4

So we see that this may be a thoroughly efficient algorithm for a base like hexadecimal. Unfortunately, no culture seems to have realized this and moved to hexadecimal for this algorithm, which is rather a pity, because it means that this observation cannot be included on WP – unless, of course, someone has noted this somewhere (perhaps in a hexadecimal-advocacy publication?). Double sharp (talk) 05:45, 1 April 2015 (UTC)

External links modified[edit]

Hello fellow Wikipedians,

I have just modified 3 external links on Ancient Egyptian multiplication. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:

When you have finished reviewing my changes, please set the checked parameter below to true or failed to let others know (documentation at {{Sourcecheck}}).

You may set the |checked=, on this template, to true or failed to let other editors know you reviewed the change. If you find any errors, please use the tools below to fix them or call an editor by setting |needhelp= to your help request.

  • If you have discovered URLs which were erroneously considered dead by the bot, you can report them with this tool.
  • If you found an error with any archives or the URLs themselves, you can fix them with this tool.

If you are unable to use these tools, you may set |needhelp=<your help request> on this template to request help from an experienced user. Please include details about your problem, to help other editors.

Cheers.—InternetArchiveBot (Report bug) 15:08, 12 October 2016 (UTC)