Historical Remarks:
-------------------
It was the Scottish mathematician John Napier (1550-1617), who invented
LOGARITHMS to simplify multiplication and division. Based on this concept,
the English mathematician William Oughtred (1574-1660) invented the useful
SLIDE RULE. J.Napier is also credited with invention of the DECIMAL POINT
for the notation of decimal fractions. But he became widely known for his
clever multiplication tool, refered as "NAPIER's BONES".
Originally made of rectangular wooden pieces, every "bone" shows the
(1..9) multiplication-table of the "bone"-number (0..9) in a special way:
The 10s-figure is separated by a diagonal from the 1s-figure. To calculate
numbers with repeated figures, every 4-sided "bone" of the (10 piece) set
carries 4 different figures - except the "index" with the figures 1..9
Here is a home-made version, made out of "Craft Sticks". Two black "index-
sticks" with figures (1..9) are 1-sided. The other (e.g. 20) sticks carry
on the back side the 9s-Complement of their front side:
(0;9) = Red, (1;8) = Yellow, (2;7) = Green, (3;6) = Blue, (4;5) = Violet.
H O W T O U S E N A P I E R ' s B O N E S
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See Example Setting: 7839 * 526
----------------------
47034 (= 6*7839)
15678 (= 2*7839)
39195 (= 5*7839)
----------------------
4123314
=======
The problem will be solved as usual (multiplying and writing from right to
left) but using the "Napier's Bones" to make it easier!
Starting with *6 use line 6 of the "index-bone" in the example setting:
index 7 8 3 9
+-------+-------+-------+-------+-------+
| | / | / | / | / |
| 6 | 4 / 2 | 4 / 8 | 1 / 8 | 5 / 4 |
| | / | / | / | / |
+-------+-------+-------+-------+-------+
4 7 0 3 4 <<<=== ( *6 )
6*9=54. The 4 (right of the diagonal in column 9) is written down. The
carry-over 5 (left of the diagonal in column 9) is added to the 8 right
of the diagonal in column 3: (8+5)=13. The 3 is written down and the
carry-over 1 is added to the next-left "diagonal-pair" (8+1)+1=10. The 0
is written down and the carry-over 1 is added to the next-left "diagonal-
pair" (2+4)+1=7. The 7 is written down. Because there is no carry-over,
the remaining 4 is written down. Proceed the same way with *2 (=line 2)
and *5 (=line 5) and indent the numbers. Add the columns for the result.
My friend WOLF BLUEMICH http://www.bluemich.net/rechner/
===========================================================================
... had made a REPLICA-SET OF "NAPIER BONES" ...
... AND also a REPLICA of WILHELM SCHICKARD's CALCULATING MACHINE ...
... SCHICKARD (1592-1635) had build this calculator in 1623 for his friend,
the astronomer JOHANNES KEPLER. For MULTIPLICATION he used NAPIER's TABLES
on cylinders, rotated to be read through the actual windows.
impressum:
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© C.HAMANN http://public.BHT-Berlin.de/hamann 11/12/13
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