Search All of the Math Forum:

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

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Replies: 86   Last Post: Jan 28, 2013 5:19 AM

 Messages: [ Previous | Next ]
 Franz Gnaedinger Posts: 330 Registered: 4/30/07
Posted: Dec 22, 2011 3:15 AM

RMP 37 - a cone

Ahmes finds a volume that measures '4 '32 hekat or 90 ro.
1 cubic cubit equals 30 hekat. 1 hekat equals 320 ro.
90 ro can be given as a cone with these measurements
(mistake '4 ro):

diameter base 7 fingers
circumference 22 fingers
height 4 palms

RMP 38 - transforming a square hekat into a cylinder

Let me begin with the subdivision of the royal cubit rod
of Amenhotep I:

1 royal cubit (52.5 cm) = 7 palms (7.5 cm) = 28 fingers
(1.875 cm) = 56 Re marks = 84 Shu marks = 112 Tefnut
marks = 140 Geb marks = 168 Nut marks = 196 Osiris marks
= 224 Isis marks = 252 Seth marks = 280 Nephtys marks =
308 Horus marks = 336 Imsety marks = 364 Hapy marks =
392 Duamutf marks = 420 Qhebsenuf marks = 468 Thoth marks

Now for RMP 38. Ahmes comes up with a funny equation:
1 hekat x 3 '7 x '22 x 7 = 1 hekat

The hekat is a measure of capacity. 30 hekat equal
1 cubic cubit. 1 hekat may be defined as a right
parallelepiped with the following measurements:

'2 royal cubit x '3 royal cubit x '5 royal cubit

or

28 Re marks x 28 Shu marks x 28 Geb marks

In Qhebsenuf marks:

210 Qm x 140 Qm x 84 Qm
cubic diagonal exactly 266 Qm

A hekat in the shape of a right parallelepiped is
well-defined. How about other shapes? Let us look again
at Ahmes' equation:

1 hekat x 3 '7 x '7 x 22 = 1 hekat

The numbers 3 '7 and '7 of 22 remind us of pi and 1/pi.
How about a hekat in the shape of a cylinder? I replace
the left hekat with the above definition:

210 Qm x 140 Qm x 84 Qm x 3 '7 x '22 x 7 = 1 hekat

Now I transform my equation:

'4 x 105 Qm x 105 Qm x 3 '7 x '11 x 3136 Qm = 1 hekat

The first term

'4 x 105 Qm x 105 Qm x 3 '7 or '4 x 7 f x 7 f x 3 '7

can be regarded as the area of a circle whose diameter
measures 105 Qhebsenuf marks or 7 fingers, while the
second term

'11 x 3136 Qm = 19 '165 fingers

can be regarded as the height of a cylinder. I leave out
the small fraction '165 and keep the height 19 fingers.
Now I can define my cylindrical hekat and quadruple-hekat
simply:

diameter 7 fingers / 14 fingers
circumference 22 fingers / 44 fingers
height 19 fingers / 19 fingers
volume 1 hekat / 4 hekat

The mistakes are tiny.

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