2 divided by 1 '3 '4 equals 1 '6 '12 '114 '228
By following Ahmes, young pupils learn how to handle unit fractions and unit fraction series, whereas advanced learners may solve a more demanding problem. Let the edges of a right parallelepiped measure
height 2 units length 1 '3 '4 units breadth 1 '6 '12 '114 '228 units
How long are the cubic diagonals?
Simply
1 '3 '4 plus 1 '6 '12 '114 '228 unitsor
1 1 plus '3 '6 plus '4 '12 plus '114 '228 unitsor
2 '2 '3 '76 units
Divide 2 by any number a and you obtain b:
2 : a = b
Using these numbers you can define a 'magic' parallelepiped of the following properties:
height 2 units length or breadth a units breadth or length b units area base or top ab square units volume 2ab cube units cubic diagonal a+b units
Let the capacity of a granary measure 500 cube cubits and find solutions of the above type. All granaries have a height of 10 royal cubits, while length and width can vary. Here is one of many solutions:
inner height 10 royal cubits or 70 palms inner length 50 palms inner width 49 palms cubic diagonal exactly 99 palms
Allow a tiny mistake and you obtain this rightparallelepiped:
(10 royal cubits = 70 palms = 280 fingers)
rp 280 by 198 by 198 fingers
cubic diagonal practically 396 fingers or 99 palms
This granary can easily be measured out using a simple rope with knots:
10 royal cubits 198 fingers 198 fingers oooo inner height inner length inner width ooo diagonal base or top cubic diagonal
(My interpretations of some 65 problems from the Rhind Mathematical Papyrus are found on my web site www.seshat.ch)
Franz Gnaedinger Zurich
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