Transcript Slide 1 - Cloudfront.net

 John Napier: Born 1550- Died 1617
 Lived in Edinburgh Scotland during time
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of Protestantism
Came from a wealthy family/background.
Man of many talents, decent values and
high intelligence (attended University of
St. Andrews at the age of 13).
Spent his time studying mathematics, and
developing new tools and formulas to
make the process of calculation easier.
Napier's free time led to invention
of Napier’s Rods, type of counting system
However most famous for his publication
of a book of Logs
 Napier’s Rod’s, a.k.a. Napier’s Bones, is a type of abacus (counting
frame) that simplified finding multiplication equations
 In addition, rods could be used to find division and square roots
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To use Napier's rods ,you need ten strips of paper each divided into 9 parts, one for each
of the first 9 multiples of the number at the top of strip as shown below
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We can use Napier’s Rods to multiply any
two numbers
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Lets start simple…
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E.g Take the equation 75 x 3
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Place the multiplier, the '7' and the '5' bone
side by side (for 75) as shown to the right.
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To calculate, sum the numbers along the
slanted diagonals of the combined bones
using the row applying to the multiplier
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For the two bones, when reading from
right to left there are three diagonals which
represent units, tens and hundreds when
the multiplier is three
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5 represents 5 units, the 1+1=2 represents 2
tens, and the 2 represents 2 hundreds.
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Adding 5 units, 2 tens and 2 hundreds
gives 225. 75 X 3 = 225
 Napier intended for his homemade
calculator to solve BIGGER
multiplication problems…
 E.g. Take the equation 84 x 24
 place the multiplier and the bones '8'
and '3' bones, for 83, side by side as
shown to the right
 To find the product first multiply by 4
and then multiply by 20
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add just as you would for long
multiplication to find the answer.
 Final answer: 1992
 Okay lets get a little more complicated: 7 x 46785399
 Once again, to solve multiply number by 7 then combined diagonal bones
through addition
 Final answer: 327,497,793
 Last example: 46785399 x 96431
 Top number should be the bigger number multiplied by the smaller
number on the side. Add entire sum
 Make sure to distinguish unit, tens, hundreds, etc. digits.
 Final answer: 4,511,562,810,969
The End