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: History of balance weights problem, 1, 3, 9 and powers of 2
Replies: 2   Last Post: Dec 5, 2012 11:47 PM

Advanced Search

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

Posts: 1,105
Registered: 12/3/04
Re: History of balance weights problem, 1, 3, 9 and powers of 2
Posted: Dec 3, 2012 2:34 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Pat,

The oldest system that I know of were used by Old Kingdom Egyptians. Binary deben and other binary weight units were used in balancing statements that rounded off a missing 1/64 unit:

1 = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + (1/64)

To my knowledge corrections to the (1/64) error, and with 1/64 being the smallest unit did not formally change to 1/320 and smaller units until the Middle Kingdom.

In the Middle Kingdom prime number denominators began to be accepted such that zero round off was allowed in most cases.

Fibonacci may have have been equally accurate, though his Arab based method, that converted rational numbers to unit fraction series followed an algorithm, did not follow the finite unit sizes used by Egyptians and Greeks.

Read Sigler's 2001 translation of the "Liber Abaci" and other medieval texts for the specifics.

Good Hunting,

Milo



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.