Napier

1
Napiers Bones

• By Shannay Witte

2
John Napier

• Born 1550 in Merchiston Castle, Edinburgh,
  ScotlandDied 4 April 1617 in Edinburgh,
  Scotland
• (John Napier Biography)
• Napier was born into a wealthy Edinburgh family
  in 1550.
• At 13, he attended the prestigious St. Andrews
  University, and went on to other universities in
  Europe. His course of studies likely included
  theology and mathematics.
• Napier returned to Scotland at 21 and began
  managing some of his father's extensive land
  holdings. He improved farming methods and helped
  settle disputes among tenants.
• When the father died in 1608, Napier moved into
  the family home, called Merchiston Castle, and
  took over as the full-time landlord.
• (Karwatka, 2001)

3
Napiers Math

• John Napier has gone down in history as the
  Scottish mathematician who invented logarithms
  (1614) and Napiers bones, an early mechanical
  calculating device for multiplication and
  division.
• (John Napier A Great Man)
• Napier's study of mathematics was only a hobby
  and in his mathematical works he writes that he
  often found it hard to find the time for the
  necessary calculations between working on
  theology. (John Napier Biography)
• Napier made a series of pencil-- length
  four-sided rods with numbers engraved on them.
  Arranging them in a particular order and reading
  the values was a way to multiply. (Kawartka,
  2001)
• John Napier acquired international fame for his
  contribution to mathematics, primarily by the
  invention of logarithms in 1614 and to a lesser
  extent by the development of Napiers Bones or
  rods and a mnemonic for formulas used in solving
  spherical triangles.
• (John Napier A Great Man)

4
The Bones

• His invention was a method for performing
  arithmetic operations by the manipulation of
  rods, called bones because they were often
  constituted from bones and printed with digits.
  Napiers rods essentially rendered the complex
  processes of multiplication and division into the
  comparatively simple tasks of addition and
  subtraction.
• (Napiers Bones All About Rods)

Napier's numbering rods were made of ivory, so
that they looked like bones which explains why
they are now known as Napier's bones. To multiply
numbers the bones were placed side by side and
the appropriate products read off. (John Napier
Biography)
5
The Whole Set of Bones
(Denholm, 1970)
6
How Bones Work

• As we can see, each rod contains ten squares the
  first is inscribed with the number associated
  with the particular rod the remaining nine are
  each bisected by a diagonal running from the
  lower left to the upper right.
• (Napiers Bones All About Rods)

7
Mathematical Examples
(Denholm, 1970)
8
Interactive Napier Applications

• Napiers Bones Java Demo
• http//www.cee.hw.ac.uk/greg/calculators/napier/d
  emo.html
• Napiers Bones Java Simulation
• http//www.cee.hw.ac.uk/greg/calculators/napier/s
  imulation.html

9
Historical Impact

• The rods were extremely popular in Napiers day
  and oddly, they constituted the Scottish
  mathematicians chief claim to glory among his
  contemporaries. It is indicative of the poor
  knowledge of arithmetic at the time, that
  extensive use was made of Napiers rods all over
  Europe, since even the simplest arithmetic
  operations were beyond the reach of most peoples
  abilities. Thus, the rods circulated widely in
  basic, middling and deluxe versions.
• (Napiers Bones All About Rods)

• Napiers invention was employed extensively by
  people whose work depended on calculations and
  numbers, such as accountants, bookkeepers etc.
  The value of Napiers rods is exemplified by the
  fact that they were still being used in primary
  schools in Britain in the mid-1960s to assist in
  teaching multiplication.
• (Napiers Bones All About Rods)