Calculator Systems

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Calculator Systems

• By Devon Hendrix
• Math 5008

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Why Question

• What are other calculator systems other than the
  abacus?
• What is a calculator?
• A calculator is a device that performs arithmetic
  operations on numbers. The simplest calculators
  can do only addition, subtraction,
  multiplication, and division.

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The Antikythera Calculator

• Sometime, between 100 BC and 65 BC, a Greek ship
  carrying a load of bronze and marble statues and
  other artifacts from Rhodes to Rome sunk close to
  the coast of Antikythera, a small island of
  Greece. 
• This interesting device, made up of 32
  gear-wheels, resembles the mechanism of an 18th
  Century clock, and was used to calculate the
  movements of the Sun and the Moon.

4
Napiers Bones

• Napiers bones is clever multiplication tool
  invented in 1617 by mathematician John Napier
  (1550-1617), of Scotland.
• The bones are a set of vertical rectangular rods,
  each one divided in 10 squares. The top square
  contains a digit and the remaining squares
  contain the first 9 multiples of the digit. Each
  multiple has its digits separated by a diagonal
  line. When a number is constructed by arranging
  side by side the rods with the corresponding
  digits on the top, then its multiple can be
  easily obtained by reading the corresponding row
  of multiples from left to right while adding the
  digits found in the parallelograms formed by the
  diagonal lines. No wonder John Napier is also the
  inventor of the logarithms, a concept used to
  change multiplication into addition.
• Napier's bones were very successful and were
  widely used in Europe until mid 1960's.

5
Schickards Machine

• The first calculating machines were built by
  gifted mathematicians moved by an intense desire
  to simplify the repetitive nature of arithmetical
  operations.
• The first known adding machine was made by
  Wilhelm Schickard (1592-1635). In 1623, designed
  and constructed a mechanical device which he
  called the Calculating Clock. Able to add and
  subtract up to six-digit numbers. The adding
  feature was devised to help performing
  multiplication with a set of Napier's cylinders
  included in the upper half of the machine.

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Slide Rule

• William Oughtred and others developed the slide
  rule in the 1600s based on the emerging work on
  logarithms by John Napier. Before the advent of
  the pocket calculator, it was the most commonly
  used calculation tool in science and engineering.
  
• The use of slide rules continued to grow through
  the 1950s and 1960s even as digital computing
  devices were being gradually introduced but
  around 1974 the electronic scientific calculator
  made it largely obsolete and most suppliers
  exited the business.

7
The Pascaline

• Blaise Pascal (1623-1662) was only 18 years old
  when he conceived the Pascaline in 1642.
• It was built on a brass rectangular box, where a
  set of notched dials moved internal wheels in a
  way that a full rotation of a wheel caused the
  wheel at the left to advance one 10th. A pin was
  used to rotate the dials. As opposed to
  Schickards machine, the wheels moved only
  clockwise and were designed only to add numbers.
  Subtraction was done by applying a cumbersome
  technique based on the addition of the nines
  complement.

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Leibniz Stepped Drum

• It was 1672 when the famous German polymath,
  mathematician and philosopher, Gottfried Wilhelm
  Von Leibniz (1646-1716) decided to build a
  machine able to perform the four basic
  arithmetical operations.
• The Stepped Reckoner, as Leibniz called his
  machine, used a special type of gear named
  Stepped Drum or Leibniz Wheel which was a
  cylinder with nine bar-shaped teeth of
  incrementing length parallel to the cylinders
  axis. As in the Pascal device, there is one set
  of wheels for each digit. This allows the user to
  slide the mobile axis so that when the drum is
  rotated it generates in the regular wheels a
  movement proportional to their relative position.
  This movement is then translated by the device
  into multiplication or division depending on
  which direction the stepped drum is rotated.

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Thomas Arithmometer

• It was not until the beginning of the 19th
  Century that the calculator became a popular
  device. This happened in 1820 when Charles Xavier
  Thomas de Colmar (1785-1870), of France, made the
  Arithmometer, a machine based on Leibnizs design
  which was capable of performing the four
  operations in a simple and reliable way. Because
  of its unidirectional drum, division and
  subtraction required setting a lever. The
  Arithmometer was also known as the Thomas
  Machine.

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Resources

• Calculator Timeline www.vintagecalculators.com/htm
  l/calculator_time-line.html
• mathforum.org/library/view/62641.html
• http//science.jrank.org/pages/1132/Calculator.htm
  l
• http//en.wikipedia.org/wiki/CalculatorsOther_ear
  ly_calculators