Napier's RodsDate: 03/05/99 at 11:38:48 From: phyllis rodin Subject: Napier's Rods I have been asked to do a math workshop on Napier's rods and I need a picture of them and some basic information. Please help! Date: 03/05/99 at 11:56:04 From: Doctor Peterson Subject: Re: Napier's Rods There is a nice site about Napier's rods at http://www.cee.hw.ac.uk/~greg/calculators/napier/ Here is an explanation from our Dr. Math archives: http://mathforum.org/dr.math/problems/crystal1.20.97.html The basic idea is that each "bone" represents a column of the multiplication table, like this (the 8 bone): +--+ |0/| |/8| 8*1 = 8 +--+ |1/| |/6| 8*2 = 16 +--+ |2/| |/4| 8*3 = 24 +--+ |3/| |/2| 8*4 = 32 +--+ |4/| |/0| 8*5 = 40 +--+ |4/| |/8| 8*6 = 48 +--+ |5/| |/6| 8*7 = 56 +--+ |6/| |/4| 8*8 = 64 +--+ |7/| |/2| 8*9 = 72 +--+ To multiply a number by a single digit, you put together the bones for its digits, then add along the diagonals in the row for the digit you are multiplying by. For example, if I line up the bones for 287, row 6 will be 2 8 7 | | | | +--+--+--+ |1/|4/|4/| 6 |/2|/8|/2| +--+--+--+ | | | | and you add like this +--+--+--+ |1/|4/|4/| /|/2|/8|/2| / +--+--+--+ / / / / 1 6 12 2 (carry the one) ------------ 1 7 2 2 so 287 * 6 = 1722. To multiply by a multiple-digit number, you would use the bones to get each row of the normal multiplication method: 287 * 26 ---- 1722 <-- what we did above 574 <-- the same, using row 2 instead of 6 ---- 7462 As you can see, Napier's bones mostly just save you from having to memorize the multiplication table; you have to do all the rest of the work yourself. They are little more than a mechanization of the "lattice method" for multiplication, which is not limited to single- digit multipliers. (You can look that up in our archives, if you are not familiar with it.) Oddly, Napier also invented the logarithm, which was the basis of the slide rule, a much more effective tool for multiplication; but his bones, which have nothing to do with logarithms, were as popular in his day as the slide rule was in mine. I think that should get you started. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ Date: 09/15/2001 at 21:30:42 From: Doctor Jodi Subject: Re: Math history There's a great page on various methods of multiplication, including Napier's Bones, at Napier's rods, abacus and slide rule - Gerold Beckers http://www.geo.tudelft.nl/mgp/people/gerold/indnap.htm For some historical information, see 1600 AD John Napier and Napier's Bones - A History of Computers http://www.maxmon.com/1600ad.htm For instructions on making Napier's bones, see Napier's Bones - Rokeby High School, Rokeby, Tasmania http://www.tased.edu.au/schools/rokebyh/curric/infotech/stage1/assign2/napier.htm This last page is part of a great site about pre-20th century computing. - Doctor Jodi, The Math Forum http://mathforum.org/dr.math/ |
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