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\begin{document}
\title{The Abacus - Then and Now}
\author[1]{TJ}%
\affil[1]{Affiliation not available}%
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\date{\today}
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\section*{The Abacus, an overview}
{\label{560010}}\par\null
What is an abacus? An abacus is an early counting device. Unlike a
modern calculator, the person operating the abacus is actually
performing the calculation and using the abacus to keep track of the
sums. The abacus dates back to Ancient Times when merchants needed a way
to keep track of goods that were bought and sold, and the abacus was one
of the counting devices that were invented to keep tallies. The
simplest~abacus is known as a counting board. This is~different from an
abacus as the counting board was just that, a board made from wood or
stone, with grooves or lines for pebbles to be moved along. The abacus
is a device that has a frame and rods for the beads to slide on, which
made it portable.
\par\null
\section*{The History of the Abacus}
{\label{119463}}\par\null
The history of the abacus can been divided into three main periods of
evolution, the Ancient Times, the Middle Ages, and the Modern Times.~
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\subsection*{Ancient Times 500 BCE - 500
CE}
{\label{943108}}
Counting and keeping track of the number of things was taking place long
before the first counting devices. Marks in bones, scratches in sand and
even crude counting tables existed, but deteriorated due to the
materials with which they had been constructed. The oldest existing
counting board is the Salamis Tablet. Made of white marble it dates back
to Greek and Roman times circa 500 CE.
\par\null
\subsection*{Middle Ages 500 CE - 1500~}
{\label{339194}}
Medieval counting boards were made with grooves or rods that the
counters were attached to. This allowed for portability and possibly
accounts for how the abacus spread throughout the world via traveling
merchants. The Chinese abacus, a Suan-pan, first appeared in 1200 CE. It
was fashioned out of a wooden frame and had metal rods. It typically had
2 beads on the upper deck and 5 beads on the lower deck.
\par\null
The introduction of the Hindu-Arabic Numbering system in Western Europe
during the late part of the Middle Ages lead to the use of paper and
pencil for arithmetic, causing the use of counting boards to all but
disappear by 1500.
\subsection*{}
{\label{980578}}
\subsection*{Modern Times 1500 -
Present}
{\label{980578}}
Based on the pair of human hands, the Russian abacus, a Shoty, is ideal
for a base-ten counting system. This abacus was also fashioned from wood
and metal rods, however it used in a vertical position whereas the
Chinese Suan-Pan and its Japanese counterpart are both set up
horizontally.~
\par\null
Also ideal for a base-ten counting system is the Japanese abacus. Around
1600 CE, the Japanese modified the Chinese Suan-Pan into what is now the
Soroban. It now contains only 1 bead on the upper deck and 4 on the
lower. The Soroban is still in use today in Japan and around the world.~
\par\null
\section*{How to use an Abacus}
The Japanese Soroban is the abacus that is still widely used today. One
can perform addition, subtraction, multiplication, and division on the
Soroban. The abacus is constructed of a rectangle frame with an upper
and lower deck. Metal or bamboo rods run vertically and contain 1 bead
on the upper deck and 4 beads on the lower deck. The upper bead, or
heavenly bead, represents the value 5. The lower deck beads, earth
beads, each represent 1. The columns of beads represent place value. A
labeled image of a Japanese Soroban Abacus is pictured below.~
\par\null
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The four mathematical operations, addition, subtraction, multiplication,
and division can all be performed using the abacus. By moving the beads
according to the values being added or subtracted and using
complimentary numbers to account for too many or too few beads, one can
calculate large arithmetic problems. Below is a link to an instructional
video that explains how to do addition on the Japanese Soroban.
\par\null
\href{https://www.youtube.com/watch?v=lQEvniBsyiU}{Click here for VIDEO
``The Japanese Soroban Abacus, Part 2: Addition''~}
\par\null\par\null
\section*{The Abacus Today}
{\label{259865}}\par\null
\begin{itemize}
\tightlist
\item
Worldwide, the abacus is an assistive technology that is used by blind
and visually impaired students as an alternative to paper and pencil
arithmetic and hand held calculators.
\item
The Soroban is still used in Japan. It is preferred by some merchants
over the hand held calculator. ~Most elementary schools have abacus as
their introduction to numbers and arithmetic. ~
\item
The video below has some interesting facts and several clips of how
abacus training is beneficial.
\end{itemize}
\par\null
\href{https://www.youtube.com/watch?v=WBPTwubFdIw}{Click here for VIDEO
``SMART Academy - Soroban Mental Arithmetic Training Academy''}
\par\null
\section*{The Mental Abacus}
{\label{133505}}\par\null
\begin{itemize}
\tightlist
\item
Many schools still teach the technique of abacus for early arithmetic
and number sense. As their skills increase, the abacus itself is
removed and the students continue to use the mental visualization of
the tool to complete computations.
\item
This mental abacus skill is put to use in many competitions, both with
the physical abacus as well as mentally.
\item
The video below shows highlights from a mental arithmetic competition.
\end{itemize}
\par\null
\href{https://www.youtube.com/watch?v=HKphPZ9YmUc}{Click here for VIDEO
``CMA Mental Arithmetic International Olympiad 2016''}
\section*{}
{\label{184344}}
\section*{Summary}
{\label{184344}}
The abacus is a counting device that has not only been used for
thousands of years throughout mathematic history, but is still used
today. Its eventual portability allowed it to be introduced to all parts
of the world. The abacus evolved into a tool that could be used across
cultures. Its design allows addition, subtraction, multiplication, and
division to be done efficiently without pencil and paper, as accurately
as the hand held calculator. The abacus although often still thought of
as an ancient device, still allows users to process operations in the
same manner that it has been done for thousands of years. Moreover, the
abacus provides students in today's classrooms with a visual sense of
numbers and a more hands-on manner of learning arithmetic.~~
\par\null
\href{http://www.mathematik.uni-marburg.de/~thormae/lectures/ti1/code/abacus/soroban.html}{Click
here for an Abacus Simulator}
\par\null\par\null\par\null
\subsection*{References}\label{references}
\par\null
CMA Mental Arithmetic International Olympiad 2016. (2016). CMA
Singapore. Retrieved April 2018,
from~\url{https://www.youtube.com/watch?v=HKphPZ9YmUc}
Fernandes, L. (2015). \emph{The Abacus}. Retrieved April 2018,
from~\url{https://www.ee.ryerson.ca/~elf/abacus/index.html}
\par\null
SMART Academy - Soroban Mental Arithmetic Training Academy. (2013).
\emph{YouTube}. Retrieved April 2018,
from~\url{https://www.youtube.com/watch?v=WBPTwubFdIw}
\par\null
The Japanese Soroban Abacus, Part 2: Addition. (2012). \emph{Adam Sahib,
YouTube}. Retrieved April 2018,
from~\url{https://www.youtube.com/watch?v=lQEvniBsyiU}
\par\null
Thormahlen, T. (2018). ~Abacus Simulator. \emph{mathematik.unimarburg}.
(Retrieved April 2018,
from~\url{http://www.mathematik.uni-marburg.de/~thormae/lectures/ti1/code/abacus/soroban.html}
\par\null
All images from Google Images
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