Talk:Ancient Egyptian multiplication
|WikiProject Mathematics||(Rated Start-class, Low-importance)|
Name change to Ethiopian Multiplication
- 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)
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 184.108.40.206 (talk) 22:01, 12 December 2014 (UTC)
Background information matches another site
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
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:
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)
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- Added archive https://web.archive.org/web/20130625181118/http://weekly.ahram.org.eg/2007/844/heritage.htm to http://weekly.ahram.org.eg/2007/844/heritage.htm
- Added archive https://web.archive.org/web/20120913011126/http://planetmath.org/encyclopedia/FirstLCMMethodRedAuxiliaryNumbers.html to http://planetmath.org/encyclopedia/FirstLCMMethodRedAuxiliaryNumbers.html
- Added archive https://web.archive.org/web/20120606142257/http://planetmath.org/encyclopedia/RationalNumbers.html to http://planetmath.org/encyclopedia/RationalNumbers.html
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