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# Ashley Smith Historical Number Systems

Math 211

by

Tweet## Ashley Sneary

on 15 August 2012#### Transcript of Ashley Smith Historical Number Systems

Historical Number Systems Roman Greek Egyptian Ashley's World Dates Current Year: nn I II Birth Year: I III III I

III III

III III Referances Egyptian

http://blog.sayan.ee/files/egypt_num.gif

http://education.ed.pacificu.edu/charlesm/courses/mathsci/numsys/numsys.html

http://gwydir.demon.co.uk/jo/numbers/egypt/multiply.htm

http://www.math.wichita.edu/history/topics/num-sys.html#egypt

C:\Users\Ashley\Pictures\hindu-arabic-numbers.gif

http://www.gap-system.org/~history/Diagrams/Hieratic.gif Greek

http://www.gap-system.org/~history/Diagrams/greek_numbers_19.gif

http://www.fargonasphere.com/piso/11-20.gif

http://www.math.wichita.edu/history/topics/num-sys.html#egypt

http://2.bp.blogspot.com/-WxJ-62iUnnA/TfSQDq_e5FI/AAAAAAAAAEg/-lXeBawLTY8/s1600/Roman+Numeral+Conversion.jpg

http://www.thegeminigeek.com/wp-content/uploads/2010/06/numbers.jpg

http://www.geez.org/Numerals/images/NumberTable2-cropped.gif Dates: Current Year: K' IB' Birth Year: IO' OI' Roman:

http://maryt.files.wordpress.com/2007/03/roman_numerals_complete.jpg

http://www.ask-math.com/images/roman-numeral-table.png

http://2.bp.blogspot.com/-WxJ-62iUnnA/TfSQDq_e5FI/AAAAAAAAAEg/-lXeBawLTY8/s1600/Roman+Numeral+Conversion.jpg

http://www.web40571.clarahost.co.uk/roman/howtheywork.htm

http://www2.inetdirect.net/~charta/bongus.gif

http://www.roman-colosseum.info/roman-life/roman-numerals.htm

http://images3.wikia.nocookie.net/__cb20110702183043/bakuganusers/images/8/8b/Roman_Numerals_Chart_1-100.png Dates: Current Year: XX XII

Birth Year: XIX XCI The origins of Egyptian mathematics was largely dependent on the changes of climate. When the climate changed in the stone age (about 3000 BC), people in Europe, had found that rivers were drying up. They found more fertile land with animals to hunt and water to drink. The place all of these peoples winded up was by rivers. New farmers had to build dikes and keep records of when the floods and rain seasons came, so they invented mathematics, calendars and almanacs. Land owners also had to keep track on how much they produced and what they owned. All who needed mathematics in their day to day operations. It’s about here that the different levels of mathematic understanding starts to show, because the relatively peaceful Nile did not demand such extensive engineering and administrative efforts, as did the more erratic Tigris and Euphrates. Egyptian Origin Egyptian Rules This is how you multiply 36 by 57 using this method in our number system, so you can follow the technique. You divide one number (here: 36) by 2 several times until you reach one.

Sometimes you can't, of course, if you have an odd number, so you then subtract 1 before halving it.

You multiply the other number by 2 the same number of times. Every line where you had the spare 1, you note what the doubled number has come to, and you add these numbers together, ignoring the others.

This is the same as the two numbers multiplied together, without using multiplication tables at all. The Greek numbering system was uniquely based upon their alphabet. The Greek alphabet came from the Phoenicians around 900 B.C. When the

Phoenicians invented the alphabet, it contained about 600 symbols. Those symbols took up too much room, so they eventually narrowed it down

to 22 symbols. The Greeks borrowed some of the symbols and made up some of their own. But the Greeks were the first people to have

separate symbols, or letters, to represent vowel sounds. Our own word "alphabet" comes from the first two letters, or numbers of the

Greek alphabet -- "alpha" and "beta." Using the letters of their alphabet enabled them to use these symbols in a more condensed version

of their old system, called Attic. The Attic system was similar to other forms of numbering systems of that era. It was based on symbols

lined up in rows and took up a lot of space to write. This might not be to bad, except that they were still carving into stone tablets,

and the symbols of the alphabet allowed them to stamp values on coins in a smaller, more condensed version.

Attic symbols = 500

= 100

= 1

= 10

= 5

For example, represented the number 849 Greek Rules Th original Greek alphabet consisted of 27 letters and was written from the left to the right. These 27 letters make up the main 27 symbols used in their numbering system. Later special symbols, which were used only for mathematics vau, koppa, and sampi, became extinct. The New Greek alphabet nowadays uses only 24 letters.

If you notice, the Greeks did not have a symbol for zero. They could string these 27 symbols together to represent any number up to 1000. By putting a comma in front of any symbol in the first row, they could now write any number up to 10,000. Greek Origin Multiplication

Egyptians method of multiplication is fairly clever, but can take longer than the modern day method. This is how they would have multiplied 5 by 29

*1 29

2 58

*4 116

1 + 4 = 5 29 + 116 = 145

When multiplying they would began with the number they were multiplying by 29 and double it for each line. Then they went back and picked out the numbers in the first column that added up to the first number (5). They used the distributive property of multiplication over addition.

29(5) = 29(1 + 4) = 29 + 116 = 145

Division

The way they did division was similar to their multiplication. For the problem 98/7 , they thought of this problem as 7 times some number equals 98. Again the problem was worked in columns.

1 7

2 *14

4 *28

8 *56

2 + 4 + 8 = 14 14 + 28 + 56 = 98

This time the the numbers in the right-hand column are marked which sum to 98 then the corresponding numbers in the left-hand column are summed to get the quotient.

So the answer is 14. 98 = 14 + 28 + 56 = 7(2 + 4 + 8) = 7*14 When Rules are Used Comparison of Hindu-Arabic and Egyptian Comparison to Hindu-Arabic and Greek Comparison of Hindu-Arabic and Roman How Greek Rules are used Forming numbers

At their simplest, numbers are formed by stringing the letters together to add up to the number required. Like this

II = 2

XXX = 30

XII = 12

CXXIII = 123

The rule is to use the biggest numeral possible at each stage, so 15 is represented by XV not VVV nor XIIIII. It follows from this rule that numerals always go from left to right in descending order. This could still lead to some very long strings. For example, using this rule 99 would be LXXXXVIIII. So at some point a new rule was invented. A smaller value letter to the left of a larger value one is subtracted. So 4 becomes IV - which is 5 minus 1 - rather than IIII.

The subtracted number must be no less than a tenth of the value of the number it is subtracted from. So an X can be placed to the left of a C or an L but not to the left of an M or a D. The correct way of looking at this rule is that each power of ten is dealt with separately. So 49 is XL IX (without the spaces), not IL

Normally, only one smaller number can be placed to the left. So 19 can be depicted XIX but 17 cannot be written XIIIX or IIIXX. However, this rule is sometimes broken for number involving an eight. On some Roman monuments and tombs IIXX for 18 is found. And in recent times times, a statue by Hamo Thornycroft called A Sower in London's Kew Gardens bears an inscription with the date MCMXXIIX meaning 1928. Such uses are not 'correct' but are found very occasionally. Roman Rules Roman Origin The origin an interesting aspect of the Etruscan numeral system is that some numbers, like in the number system of the Romans, are represented as partial subtractions. The system is based on the number 10 - so no doubt this ancient counting system was originally based based on a counting method using the fingers. A single stroke of the pen would represent one finger. When The Rules are Used Roman Chart 1 to 100 Greek Chart 1 to 100 Egyptian Chart 1 to 100 Ashley's Origin Then the Larger the nu,ber the small the answer when subtracting, This helps to understand who you take away from other amounts with money or grading papers. Ashley's Rules and why they are used When you have $50 and you take $30 away to pay a bill you have $20 left. This will help you when you need to know how much you will have left. Or when your grading a paper out of 100 points if the students gets 80 points out of 100 you lost 20 points and they have an 80%. How the Ashley's World Works 100-20=80

50-30=20 Hindu-Arabic Comparison They are compared by the base 10. Dates Current Year: 2012

Birth Year: 1991

Full transcriptIII III

III III Referances Egyptian

http://blog.sayan.ee/files/egypt_num.gif

http://education.ed.pacificu.edu/charlesm/courses/mathsci/numsys/numsys.html

http://gwydir.demon.co.uk/jo/numbers/egypt/multiply.htm

http://www.math.wichita.edu/history/topics/num-sys.html#egypt

C:\Users\Ashley\Pictures\hindu-arabic-numbers.gif

http://www.gap-system.org/~history/Diagrams/Hieratic.gif Greek

http://www.gap-system.org/~history/Diagrams/greek_numbers_19.gif

http://www.fargonasphere.com/piso/11-20.gif

http://www.math.wichita.edu/history/topics/num-sys.html#egypt

http://2.bp.blogspot.com/-WxJ-62iUnnA/TfSQDq_e5FI/AAAAAAAAAEg/-lXeBawLTY8/s1600/Roman+Numeral+Conversion.jpg

http://www.thegeminigeek.com/wp-content/uploads/2010/06/numbers.jpg

http://www.geez.org/Numerals/images/NumberTable2-cropped.gif Dates: Current Year: K' IB' Birth Year: IO' OI' Roman:

http://maryt.files.wordpress.com/2007/03/roman_numerals_complete.jpg

http://www.ask-math.com/images/roman-numeral-table.png

http://2.bp.blogspot.com/-WxJ-62iUnnA/TfSQDq_e5FI/AAAAAAAAAEg/-lXeBawLTY8/s1600/Roman+Numeral+Conversion.jpg

http://www.web40571.clarahost.co.uk/roman/howtheywork.htm

http://www2.inetdirect.net/~charta/bongus.gif

http://www.roman-colosseum.info/roman-life/roman-numerals.htm

http://images3.wikia.nocookie.net/__cb20110702183043/bakuganusers/images/8/8b/Roman_Numerals_Chart_1-100.png Dates: Current Year: XX XII

Birth Year: XIX XCI The origins of Egyptian mathematics was largely dependent on the changes of climate. When the climate changed in the stone age (about 3000 BC), people in Europe, had found that rivers were drying up. They found more fertile land with animals to hunt and water to drink. The place all of these peoples winded up was by rivers. New farmers had to build dikes and keep records of when the floods and rain seasons came, so they invented mathematics, calendars and almanacs. Land owners also had to keep track on how much they produced and what they owned. All who needed mathematics in their day to day operations. It’s about here that the different levels of mathematic understanding starts to show, because the relatively peaceful Nile did not demand such extensive engineering and administrative efforts, as did the more erratic Tigris and Euphrates. Egyptian Origin Egyptian Rules This is how you multiply 36 by 57 using this method in our number system, so you can follow the technique. You divide one number (here: 36) by 2 several times until you reach one.

Sometimes you can't, of course, if you have an odd number, so you then subtract 1 before halving it.

You multiply the other number by 2 the same number of times. Every line where you had the spare 1, you note what the doubled number has come to, and you add these numbers together, ignoring the others.

This is the same as the two numbers multiplied together, without using multiplication tables at all. The Greek numbering system was uniquely based upon their alphabet. The Greek alphabet came from the Phoenicians around 900 B.C. When the

Phoenicians invented the alphabet, it contained about 600 symbols. Those symbols took up too much room, so they eventually narrowed it down

to 22 symbols. The Greeks borrowed some of the symbols and made up some of their own. But the Greeks were the first people to have

separate symbols, or letters, to represent vowel sounds. Our own word "alphabet" comes from the first two letters, or numbers of the

Greek alphabet -- "alpha" and "beta." Using the letters of their alphabet enabled them to use these symbols in a more condensed version

of their old system, called Attic. The Attic system was similar to other forms of numbering systems of that era. It was based on symbols

lined up in rows and took up a lot of space to write. This might not be to bad, except that they were still carving into stone tablets,

and the symbols of the alphabet allowed them to stamp values on coins in a smaller, more condensed version.

Attic symbols = 500

= 100

= 1

= 10

= 5

For example, represented the number 849 Greek Rules Th original Greek alphabet consisted of 27 letters and was written from the left to the right. These 27 letters make up the main 27 symbols used in their numbering system. Later special symbols, which were used only for mathematics vau, koppa, and sampi, became extinct. The New Greek alphabet nowadays uses only 24 letters.

If you notice, the Greeks did not have a symbol for zero. They could string these 27 symbols together to represent any number up to 1000. By putting a comma in front of any symbol in the first row, they could now write any number up to 10,000. Greek Origin Multiplication

Egyptians method of multiplication is fairly clever, but can take longer than the modern day method. This is how they would have multiplied 5 by 29

*1 29

2 58

*4 116

1 + 4 = 5 29 + 116 = 145

When multiplying they would began with the number they were multiplying by 29 and double it for each line. Then they went back and picked out the numbers in the first column that added up to the first number (5). They used the distributive property of multiplication over addition.

29(5) = 29(1 + 4) = 29 + 116 = 145

Division

The way they did division was similar to their multiplication. For the problem 98/7 , they thought of this problem as 7 times some number equals 98. Again the problem was worked in columns.

1 7

2 *14

4 *28

8 *56

2 + 4 + 8 = 14 14 + 28 + 56 = 98

This time the the numbers in the right-hand column are marked which sum to 98 then the corresponding numbers in the left-hand column are summed to get the quotient.

So the answer is 14. 98 = 14 + 28 + 56 = 7(2 + 4 + 8) = 7*14 When Rules are Used Comparison of Hindu-Arabic and Egyptian Comparison to Hindu-Arabic and Greek Comparison of Hindu-Arabic and Roman How Greek Rules are used Forming numbers

At their simplest, numbers are formed by stringing the letters together to add up to the number required. Like this

II = 2

XXX = 30

XII = 12

CXXIII = 123

The rule is to use the biggest numeral possible at each stage, so 15 is represented by XV not VVV nor XIIIII. It follows from this rule that numerals always go from left to right in descending order. This could still lead to some very long strings. For example, using this rule 99 would be LXXXXVIIII. So at some point a new rule was invented. A smaller value letter to the left of a larger value one is subtracted. So 4 becomes IV - which is 5 minus 1 - rather than IIII.

The subtracted number must be no less than a tenth of the value of the number it is subtracted from. So an X can be placed to the left of a C or an L but not to the left of an M or a D. The correct way of looking at this rule is that each power of ten is dealt with separately. So 49 is XL IX (without the spaces), not IL

Normally, only one smaller number can be placed to the left. So 19 can be depicted XIX but 17 cannot be written XIIIX or IIIXX. However, this rule is sometimes broken for number involving an eight. On some Roman monuments and tombs IIXX for 18 is found. And in recent times times, a statue by Hamo Thornycroft called A Sower in London's Kew Gardens bears an inscription with the date MCMXXIIX meaning 1928. Such uses are not 'correct' but are found very occasionally. Roman Rules Roman Origin The origin an interesting aspect of the Etruscan numeral system is that some numbers, like in the number system of the Romans, are represented as partial subtractions. The system is based on the number 10 - so no doubt this ancient counting system was originally based based on a counting method using the fingers. A single stroke of the pen would represent one finger. When The Rules are Used Roman Chart 1 to 100 Greek Chart 1 to 100 Egyptian Chart 1 to 100 Ashley's Origin Then the Larger the nu,ber the small the answer when subtracting, This helps to understand who you take away from other amounts with money or grading papers. Ashley's Rules and why they are used When you have $50 and you take $30 away to pay a bill you have $20 left. This will help you when you need to know how much you will have left. Or when your grading a paper out of 100 points if the students gets 80 points out of 100 you lost 20 points and they have an 80%. How the Ashley's World Works 100-20=80

50-30=20 Hindu-Arabic Comparison They are compared by the base 10. Dates Current Year: 2012

Birth Year: 1991