Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » Inactive » math-history-list

Topic: Breaking the RMP 2/n table by decoding a 500 AD Coptic document
Replies: 11   Last Post: Sep 14, 2011 6:38 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ] Topics: [ Previous | Next ]
Milo Gardner

Posts: 1,105
Registered: 12/3/04
Re: Breaking the RMP 2/n table by decoding a 500 AD Coptic document
Posted: Jun 17, 2011 6:14 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

A summary of two 500 AD Coptic n/p tables follow:

n/17 Akhmim P. Value LCM (m/m) used Ahmes 1650 BC method*
---- -------------------------------------
2/17 = 12' 51' 68' = 2/17(12/12) = 24/204 = (17 + 4 + 3)/204
3/17 = 12' 17' 51' 68' = 3/17(12/12) = 36/204 = (17 + 12 + 4 + 3)/204
4/17 = 12' 15'17' 68' 85' = 4/17(60/60) = 240/1020 = (85 + 68 + 60 + 15 + 12)/102
5/17 = 4' 34' 68' = 5/17(4/4) = 20/68 = (17 + 2 + 1)/68
6/17 = 3' 51' = 6/17(3/3) = 18/68 = (17 + 1)/68
7/19 = 3' 17' 51' = 7/17(3/3) = 21/51 = (17 + 3 + 1)/51
8/17 = 3' 15' 17' 85' = 8/17(30/30) = 240/510 = (170 + 34 + 30 + 6)/510
9/17 = 1/2 34' = 9/17(2/2) = 18/34 = (17 + 1)/34
10/17 = 1/2 17' 34' = 10/17(2/2)= 20/34 = (17 + 2 + 1)/34
11/17 = 1/2 12' 34' 51' 68' = 11/17(12/12) = 132/204 =(102 + 17 + 6 + 4 + 3)/204
12/17 = 1/2 12' 17' 34' 51' 68' = 12/17(12/12) = 144/204 =(102 + 17 + 12 + 6 + 4 + 3)/204
13/17 = 1/2 4' 68' = 13/17(4/4) = 52/68 = (34 + 17 + 1)/68
14/17 = 1/2 4' 17' 68' = 14/17(4/4)= 56/68 = (34 + 17 + 4 + 1)/68
15/17 = 1/2 3' 34' 51' = 15/17(6/6) = 90/102 = (51 + 34 + 3 + 2)/102
16/17 = 1/2 3' 17' 34' 51' = 15/17(6/6) = 96/102 = (51 + 34 + 6 + 3 + 2)/102

* http://rmprectotable.blogspot.com/

The AP scribe used seven LCM m = 2, 3, 4, 6, 10,12 and 60 that scaled n/17 table members to concise unit fractions series. The scribal method dates to the Egyptian Middle Kingdom, at least 2,100 years earlier.



n/19 Akhmim P. value LCM (m/m) followed Ahmes 1650 BC method*
----- --------------------- ------------------------------------
2/19 = 10' 190' = 2/19(10/10) = 20/190 = (19 + 1)/190
3/19 = 15' 20' 57' 76' 95' = 3/19(120/120) = 360/2280 = (152 + 119 + 40 + 30 + 19)/2280
4/19 = 5' 95' = 4/19(5/5) = 20/95 = (19 + 1)/95
5/19 = 4' 76' = 5/19(4/4) = 20/76 = (19 + 1)/76
6/19 = 4' 19' 76' = 6/19(4/4) = 24/76 = (19 + 4 + 1)/76
7/19 = 3' 38' 114' = 7/19(6/6) = 42/114 = (38 + 3 + 1)/114
8/19 = 3' 30' 38' 57' 95' = 8/19(30/30) = 240/570 = (190 + 19 + 15 + 10 + 6)/570
9/19 = 3' 12' 38' 57' 76' = 9/19(12/12) = 108/228 = (76 + 19 + 6 + 4 + 3)/228
10/19 = 1/2 38' = 10/19(2/2) = 20/38 = (19 + 1)/38
11/19 = 1/2 19' 38' = 11/19(2/2) = 22/38 = (19 + 2 + 1)/38
12/19 = 1/2 12' 38' 76' 114' = 12/19(12/12) = 144/228 = (114 + 19 + 6 + 3 + 2)/228
13/19 = 3" 57' = 13/19(3/3) = 39/57 = (38 + 1)/57
14/19 = 3" 19' 57' = 14/19(3/3)= 42/57 = (38 + 3 + 1)/57
15/19 = 1/2 4' 38' 76' = 15/19(4/4) = 60/76 = (38 + 19 + 2 + 1)/76
16/19 = 1/2 4' 19' 38' 76' = 16/19(4/4) = 64/76 = (38 + 19 + 4 + 2 + 1)/76
17/19 = 1/2 3' 30' 57' 95' = 17/19(30/30) = 510/570 =(285 + 190 + 19 + 10 + 6)/570
18/19 = 1/2 3' 12' 57' 76' = 18/19(12/12) = 216/228 = (114 + 38 + 19 + 4 + 3)/228

* http://rmprectotable.blogspot.com/

The AP scribe used eight LCM m = 2, 3, 4, 6, 10, 12, 30 and 120 that scaled n/19 table members to concise unit fraction series that followed Ahmes' 2,100 year older methodology, that also followed the Greek ciphered fraction system: 1/p = p'



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.