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: Ariadne's thread
Replies: 86   Last Post: Jan 28, 2013 5:19 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Franz Gnaedinger

Posts: 330
Registered: 4/30/07
Re: Ariadne's thread
Posted: Dec 21, 2011 3:35 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

One single equation containing three variables can't be
solved. Ahmes did not use algebra. He used algorithms
or step by step procedures that required a good knowledge
of conversions of 1 into a variety of unit fraction series
- the more the better. Beginners had to learn those
algorithms and conversions. If they excelled - when they
could perform the arithmetical operations 'in their sleep' -
they were taken to the higher levels of challenging problems
and hidden theorems enveloped in the same numbers. We can
reach the advanced levels and unveil the secrets promised
by Ahmes in the opening lines of the Rhind Mathematical
Papyrus (copy of a lost scroll of the Middle Kingdom from
around 1850 BC) playing with the numbers, recognizing to
our surprise that the same problems could have been used
for beginners and 'college' classes and 'graduates' alike.
Picture that we could use the same math textbook from
primary school to seminary ...

RMP 36 - a pair of granaries

3 '3 '5 times '4 '53 '106 '212 equals 1

Imagine a square whose diagonal measures 2 royal cubits.
Its area measures 2 square cubits.

Imagine a circle whose diagonal measures 3 royal cubits.
Using the value '135 of 424 for pi, the area of the
circle measures 7 '15 square cubits.

6/2 (plus 22/7) 28/9 ... 424/135

Build a granary on the square (inner diagonal 2 royal
cubits). Build a granary on the circle (inner diameter
3 royal cubits).

Fill the round granary to a height of 1 royal cubit.
You will need 53 quadruple-hekat or 212 hekat of barley.
Fill 212 hekat of grain in the square granary. The barley
will reach a height of 3 '3 '5 royal cubits.

Fill the square granary to a height of 1 royal cubit. You
will need 2 cubic cubits or 3 khar or 15 quadruple-hekat
or 60 hekat of barley. Fill 60 hekat of barley in the
round granary. It will reach a height of '4 '53 '106 '212
royal cubits.


Date Subject Author
11/17/11
Read Ariadne's thread
Franz Gnaedinger
11/17/11
Read Re: Ariadne's thread
Milo Gardner
11/18/11
Read Re: Ariadne's thread
Franz Gnaedinger
11/18/11
Read Re: Ariadne's thread
Milo Gardner
11/19/11
Read Re: Ariadne's thread
Franz Gnaedinger
11/19/11
Read Re: Ariadne's thread
Milo Gardner
11/20/11
Read Re: Ariadne's thread
Franz Gnaedinger
11/20/11
Read Re: Ariadne's thread
Milo Gardner
11/20/11
Read Re: Ariadne's thread
Milo Gardner
11/21/11
Read Re: Ariadne's thread
Franz Gnaedinger
11/22/11
Read Re: Ariadne's thread
Franz Gnaedinger
11/22/11
Read Re: Ariadne's thread
Milo Gardner
11/23/11
Read Re: Ariadne's thread
Franz Gnaedinger
11/24/11
Read Re: Ariadne's thread
Franz Gnaedinger
11/24/11
Read Re: Ariadne's thread
Franz Gnaedinger
11/24/11
Read Re: Ariadne's thread
Franz Gnaedinger
11/24/11
Read Re: Ariadne's thread
Milo Gardner
11/25/11
Read Re: Ariadne's thread
Franz Gnaedinger
11/26/11
Read Re: Ariadne's thread
Franz Gnaedinger
12/2/11
Read Re: Ariadne's thread
Franz Gnaedinger
12/2/11
Read Re: Ariadne's thread
Milo Gardner
12/3/11
Read Re: Ariadne's thread
Franz Gnaedinger
12/4/11
Read Re: Ariadne's thread
Franz Gnaedinger
12/4/11
Read Re: Ariadne's thread
Milo Gardner
12/5/11
Read Re: Ariadne's thread
Franz Gnaedinger
12/5/11
Read Re: Ariadne's thread
Milo Gardner
12/7/11
Read Re: Ariadne's thread
Franz Gnaedinger
12/8/11
Read Re: Ariadne's thread
Milo Gardner
12/10/11
Read Re: Ariadne's thread
Franz Gnaedinger
12/12/11
Read Re: Ariadne's thread
Franz Gnaedinger
12/12/11
Read Re: Ariadne's thread
Milo Gardner
12/13/11
Read Re: Ariadne's thread
Franz Gnaedinger
12/13/11
Read Re: Ariadne's thread
Milo Gardner
12/15/11
Read Re: Ariadne's thread
Franz Gnaedinger
12/15/11
Read Re: Ariadne's thread
Milo Gardner
12/15/11
Read Re: Ariadne's thread
Milo Gardner
12/16/11
Read Re: Ariadne's thread
Franz Gnaedinger
12/16/11
Read Re: Ariadne's thread
Milo Gardner
12/18/11
Read Re: Ariadne's thread
Franz Gnaedinger
12/18/11
Read Re: Ariadne's thread
Milo Gardner
12/19/11
Read Re: Ariadne's thread
Franz Gnaedinger
12/20/11
Read Re: Ariadne's thread
Franz Gnaedinger
12/20/11
Read Re: Ariadne's thread
Milo Gardner
12/21/11
Read Re: Ariadne's thread
Franz Gnaedinger
12/22/11
Read Re: Ariadne's thread
Franz Gnaedinger
12/23/11
Read Re: Ariadne's thread
Franz Gnaedinger
12/24/11
Read Re: Ariadne's thread
Franz Gnaedinger
12/29/11
Read Re: Ariadne's thread
Franz Gnaedinger
1/2/12
Read Re: Ariadne's thread
Franz Gnaedinger
1/3/12
Read Re: Ariadne's thread
Milo Gardner
1/4/12
Read Re: Ariadne's thread
Franz Gnaedinger
11/28/11
Read Re: Ariadne's thread
Velev, Petyr
1/6/12
Read Re: Ariadne's thread
Franz Gnaedinger
1/6/12
Read Re: Ariadne's thread
Milo Gardner
1/9/12
Read Re: Ariadne's thread
Franz Gnaedinger
1/17/12
Read Re: Ariadne's thread
Franz Gnaedinger
1/19/12
Read Re: Ariadne's thread
Franz Gnaedinger
1/19/12
Read Re: Ariadne's thread
Milo Gardner
1/27/12
Read Re: Ariadne's thread
Franz Gnaedinger
2/10/12
Read Re: Ariadne's thread
Franz Gnaedinger
2/28/12
Read Re: Ariadne's thread
Franz Gnaedinger
3/2/12
Read Re: Ariadne's thread
Franz Gnaedinger
3/23/12
Read Re: Ariadne's thread
Franz Gnaedinger
3/24/12
Read Re: Ariadne's thread
Milo Gardner
4/9/12
Read Re: Ariadne's thread
Franz Gnaedinger
4/10/12
Read Re: Ariadne's thread
Franz Gnaedinger
4/13/12
Read Re: Ariadne's thread
Franz Gnaedinger
4/17/12
Read Re: Ariadne's thread
Franz Gnaedinger
4/18/12
Read Re: Ariadne's thread
Franz Gnaedinger
4/18/12
Read Re: Ariadne's thread
Franz Gnaedinger
5/5/12
Read Re: Ariadne's thread
Franz Gnaedinger
5/7/12
Read Re: Ariadne's thread
Franz Gnaedinger
5/7/12
Read Re: Ariadne's thread
Milo Gardner
5/8/12
Read Re: Ariadne's thread
Franz Gnaedinger
5/8/12
Read Re: Ariadne's thread
Milo Gardner
5/8/12
Read Re: Ariadne's thread
Franz Gnaedinger
5/8/12
Read Re: Ariadne's thread
Franz Gnaedinger
5/9/12
Read Re: Ariadne's thread
Franz Gnaedinger
5/10/12
Read Re: Ariadne's thread
Franz Gnaedinger
8/14/12
Read Re: Ariadne's thread
Franz Gnaedinger
1/13/13
Read Re: Ariadne's thread
Franz Gnaedinger
1/19/13
Read Re: Ariadne's thread
Franz Gnaedinger
1/23/13
Read Re: Ariadne's thread
Franz Gnaedinger
1/23/13
Read Re: Ariadne's thread
Franz Gnaedinger
1/24/13
Read Re: Ariadne's thread
Franz Gnaedinger
1/26/13
Read Re: Ariadne's thread
Franz Gnaedinger
1/28/13
Read Re: Ariadne's thread
Franz Gnaedinger

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.