Ancient Number Systems A Brief Overview

In The Beginning One and Many Men needed new numbers, so they strung them together The Bacairi and Bororo of Brazil string numbers-words together - one, two, two and one, two and two, etc.

Dem Dry Bones Tally Sticks Ishango Bone - 18,000 BC 30,000 year-old wolf bone in Czechoslovakia - 55 notches arranged in groups of 5

Counting with Body Parts 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

Why Count? Property Trading Time Measuring Etc…

Egyptian Numerals

Overview Possible the first to practice science Base 10 Not positional, had no zero Measuring and Surveying Nile floods Taxes Mostly they used geometry

Symbols

Fractions and Operations 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

Babylonian Numerals

Overview Sexagesimal (base 60) system Measured circles and spheres using 360 equal parts. Famous for astronomical observations and calculations They invented the abacus

Overview Continued First known positional system - Numbers arranged in columns 60 is a superior highly composite number Divisible 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:

Symbols

Positional System

Roman Numerals

Overview 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

Subtraction Rules 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

Legacy of Roman Numerals 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 Continued Monarchs and Popes (Elisabeth II, Pope Benedict XVI) Generational Suffixes (Ex: Thurston Howell III) Year of construction on cornerstones And many more uses

Greek Numbers

Overview 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)

Symbols

Mayan numerals

Overview Place value (positional) number system Base 20 (vigesimal) They have a 0 They used rows instead of columns Shells, sticks and pebbles

Symbols

Operations They had addition and subtraction You will have a chance to try operations with Mayan Numerals later this week

Calendar 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.

Chinese Numerals

Overview 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

Shang Oracle Bone 14th Century BC

Counting Rod Numerals

Zero 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.

Hindu-arabic numerals

Overview 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

Fibonacci 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”)

“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