A Brief Overview. One and Many Men needed new numbers, so they strung them together The Bacairi and...
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A Brief Overview
Ancient Number Systems
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One and Many Men needed new numbers, so they strung
them togetherThe Bacairi and Bororo of Brazil string
numbers-words together - one, two, two and one, two and two, etc.
In The Beginning
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Tally Sticks Ishango Bone
- 18,000 BC
30,000 year-old wolf bone in Czechoslovakia - 55 notches arranged in groups of 5
Dem Dry Bones
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Five was popular “Fiving” was used by the Greeks to describe
tallying Our decimal system started by counting on
our fingers Some ancient cultures used a base-20 or
vigesimal system- This came from counting fingers and
toes
Counting with Body Parts
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Property Trading Time Measuring Etc…
Why Count?
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Egyptian Numerals
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Possible the first to practice science Base 10 Not positional, had no zero Measuring and Surveying Nile floods Taxes Mostly they used geometry
Overview
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Symbols
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They had ways of expressing unit fractions (the numerator is 1) and common fractions such as 3/4 and 2/3
They also had addition and subtraction
Fractions and Operations
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Babylonian Numerals
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Sexagesimal (base 60) system Measured circles and spheres using 360
equal parts. Famous for astronomical observations and
calculations They invented the abacus
Overview
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First known positional system - Numbers arranged in columns
60 is a superior highly composite numberDivisible by 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, and
30 Powers of 60 instead of 10 No symbol for 0, instead used a different
place holder:
Overview Continued
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Symbols
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Positional System
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Roman Numerals
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Written using letters from the Latin alphabet
This is a biquinary system (base 10 with sub-base 5)
Use an additive and subtractive system Example: - IV = 4, 1 before 5
Overview
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Subtract only powers of 10, such as I (100), X (101) or C (102). VL = 45 is not allowed
Subtract only one numeral from one numeral. Write VIII for 8, not IIX. 19 is XIX, IXX
Don’t subtract a letter from another letter more than 10 times greater. MIM is “illegal”, you can only subtract I from V or X, X from L or C, and C from M
Subtraction Rules
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Hour marks on timepieces Sequels of movies, video games, and other
works (ex: Star Wars IV: A New Hope) Book volume and chapter numbers Page numbering and outlines Occurrances of large recurring events:
-The Olympic Games (XXXI Winter Games)
- The Super Bowl (XLVII)
Legacy of Roman Numerals
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Monarchs and Popes (Elisabeth II, Pope Benedict XVI)
Generational Suffixes (Ex: Thurston Howell III)
Year of construction on cornerstones And many more uses
Legacy Continued
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Greek Numbers
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Used letters as numbers Didn’t have zero You had to memorize addition facts Multiplication was worse Numerology was common because they used
their letters for their alphabet Now we use Greek letters for specific
numbers - π and ф (the golden ratio)
Overview
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Symbols
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Mayan numerals
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Place value (positional) number system Base 20 (vigesimal) They have a 0 They used rows instead of columns Shells, sticks and pebbles
Overview
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Symbols
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They had addition and subtraction You will have a chance to try operations with
Mayan Numerals later this week
Operations
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The Solar Calendar in the Calendar Round; called the Haab, is extremely accurate
Each month was 20 days and they had 18 months
There was a 5 day period called Uayeb or Wayeb that was unlucky
The Western calendar was created with no year 0
- This caused a controversy of the precise start of the millennium.
Calendar
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Chinese Numerals
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Mathematics was considered both pracitcal and spiritual
- Covered everything from administration and water control to religion and astronomy
Art of Calculation Base 10 “Nine Chapter on the Mathematical Art” 200
BC
Overview
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Shang Oracle Bone 14th Century BC
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Counting Rod Numerals
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They understood zero, but didn’t have a symbol
To deal with a placeholder, they would use a reckoning board, with an empty square to signify 0.
Zero
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Hindu-arabic numerals
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These are the numbers we use now Positional decimal system A stone inscription found at Chaturbhuja
Temple at Gwalior in India is the first instance of 0.
The oldest known writing using a fully develop numeration system appears in a book from AD 825 by Persian Mathematician al-Khowarizmi
Overview
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Fibonacci is also know as Leonardo of Pisa is an Italian mathematician
Made Hindu-Arabic Numerals popular in Europe
Liber Abaci (“The Book of Calculation”)
Fibonacci
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“My father was a public scribe of Bejaia [Algeria], where he worked in Customs, defending the interests of Pisan merchants who made their
fortune there. He made me learn how to use the abacus when I was still a child because he saw how I would benefit from this in later life. In this way I learned the are of counting using the nine Indian figures…as follows: 9, 8, 7, 6, 5, 4, 3, 2, 1, … With these nine numerals, and with this sign 0, called
zephirum in Arabic, one writes all the numbers one wishes. - Leonardo of Pisa