Historical+Perspective

**Historical Perspective**

"The art of counting and recording number is one of the oldest mathematical skills for which we have evidence. In fact, there is some evidence that it preceded a written language" (Wall, pg. 11).

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 The invention of numbers was thought to have start many thousands of years ago, and used in as a one to one correspondence to keep track of quantity of livestock other valuable possessions. As the demand for numbers became more necessary, people started creating systems that symbolized quantities, moving numbers from their physical properties to their abstract properties. Still, these values were used to keep record of livestock, property, and trade. For this reason, numbers were initially only whole numbers and perhaps rational numbers.

As numbers became a more practical part of life, civilizations began to work with them. The Babylonians began testing claims and were one of the first people to develop a system of taking the square root. The Greeks began looking at geometric structures. As math evolved to become more abstract, ideas became more complex and popular. None of these more complex notions would even be rational or valid without the invention of numbers. So, let's take a trip down memory lane and review some of the early ways of counting.

**Tally Stick**
 Used most likely with the one-to-one correspondence system, the tally stick used marks to denote numbers. It was probably one of the first numeric representation systems.





**Egyptian Recording System**
 One of the earliest recording systems was the Egyptian recording systems. Using Egyptian hieroglyphics, this civilization's system rounded of at decimal numbers and did not have a way to record irrational numbers. Their system was a base 10 system, like our system today. Below, you will find the hieroglyphics that correspond with the numbers.



**Strike**: Used for numerals 1 - 9. Each strike symbolized a number 1-9. Thus, 5 would look like this: ||| || **Heel Bone**: Used to represent collections of 10. **Coil of Rope**: Used to represent collections of 100. **Water Lilly**: Used to represent collections of 1,000. **Bent Finger**: Used to represent collections of 10,000. <span style="display: block; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 110%; text-align: left;">**Tadpole**: Used to represent collections of 100,000. <span style="display: block; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 110%; text-align: left;">**Astonished Man**: Used to represent collections of 1,000,000.

<span style="color: #d15b17; display: block; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 120%; text-align: left;">**The Roman System**
<span style="display: block; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 110%; text-align: left;">The Roman system as been used is thought to have been in use as early as 800BC. It is a decimal system, but not necessarily positional, for there is no value representing the number zero. After the fall of the Roman Empire, Roman Numerals were widely abandoned and replaced with the Arabic system that we use today. Below is an index of Roman Numerals:

<span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 140%; text-align: center;"> **I II V X L C D M** <span style="display: block; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 110%; text-align: center;">1 2 5 10 50 100 500 1000 **<span style="display: block; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 110%; text-align: center;">Roman Numerals ** <span style="display: block; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 110%; text-align: left;">Want to convert any number to Roman fast? [|Click here!] <span style="display: block; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 110%; text-align: left;">(The converter is the purple box on the right-hand side of the page!)

<span style="color: #d15b17; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif;">Attic Greek Numerals
<span style="display: block; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 110%; text-align: left;">Attic Greek numerals were thought to have been used as early as 700 AD and are similar to the Roman numeral system. This is a simple grouping system. The numerals can be found below:





<span style="color: #d15b17; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 130%;">**Chinese - Japanese System**
<span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 110%;">The Chinese-Japanese system is also a multiplicative grouping system where numbers are written vertically:



<span style="color: #d15b17; display: block; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 120%; text-align: left;">**Other Systems**
<span style="display: block; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 110%; text-align: left;">There are other systems that can be used, but not all can be demonstrated here. Other systems are the Greek Alphabetic system which uses 27 symbols to represent numbers 1-9, 10-90, and 100-900. To learn more about the Greek Alphabetic system, [|click here]. The Gorbar Arabic system is one that closely resembles the numerals that we use today. See page 14 in //Number Theory// to view these numbers.

<span style="display: block; font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif; font-size: 110%; text-align: left;">Sources: <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif;">Creative Commons. (Designer). (2008). //500 attic greek//. [Print Photo]. Retrieved from http://commons.wikimedia.org/wiki/Category:Greek_numeral <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif;">Deacon, S. (Designer). (2010). //Chinese-japanese numbers//. [Web Photo]. Retrieved from http://www.importanceoflanguages.com/LearnJapanese/rocket-japanese/ <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif;">Forex, J. (Designer). (2011). //Tally Sticks//. [Web Photo]. Retrieved from http://falconlog.blogspot.com/2011/02/modern-money-mechanics-work-in-progress.html <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif;">Gleason, D. (Designer). (2008). //Attic greek numerals//. [Print Photo]. Retrieved from http://www.jesus8880.com/chapters/gematria/greek-numerals.htm <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif;">Wall, E. (2010). //Number theory for elementary school teachers//. Boston: McGraw Hill Higher Education. <span style="font-family: 'Palatino Linotype','Book Antiqua',Palatino,serif;">Yanze, D. (Photographer). (2009). //Egyptian number system//. [Web Photo]. Retrieved from http://ancientegypt3.blogspot.com/2009/06/egyptian-numeration.html