A Brief Overview

Ancient Number Systems

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

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

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

Property Trading Time Measuring Etc…

Why Count?

Egyptian Numerals

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

Overview

Symbols

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

Babylonian Numerals

Sexagesimal (base 60) system Measured circles and spheres using 360

equal parts. Famous for astronomical observations and

calculations They invented the abacus

Overview

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

Symbols

Positional System

Roman Numerals

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

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

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

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

Greek Numbers

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

Symbols

Mayan numerals

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

Overview

Symbols

They had addition and subtraction You will have a chance to try operations with

Mayan Numerals later this week

Operations

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

Chinese Numerals

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

Shang Oracle Bone 14th Century BC

Counting Rod Numerals

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

Hindu-arabic numerals

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

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

“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