-Emily & Mackenzie Ancient Number Systems The Different types of numerical systems Terminology of ancient numbers Where did numbers come about? Tally numeral system How did we get the looks of our modern day numbers? Greek Numeral System Roman Numeral System There are many variations of ancient number systems Fingers, rocks, sticks or eyes were used to represent numbers.

Some of the terminology that were used were: flocks of sheep, heaps of grain, or lots of people.

It is said that the first known use of numbers dates back to around 30,000 BC The Chinese had one of the oldest systems of numerals that were based on stick shapes If you count the number of the angles of the drawn figures above you will see how these numbers came about. Tallying is one of the earliest methods of keeping a record of quantities and appears in many early cultures. The Ancient Roman numerals uses combinations of letters from the Latin alphabet to signify number values. Hindu-Arabic numeral system

Tally numeral system

Egyptian numeral system

Roman numeral system

Babylonian numeral system

Mayan numeral system

Chinese numeral system

Greek numeral system For example: The numbers we use (1, 2, 3, 4, etc.) are known as "Hindu-Arabic" numbers.

The Arabs popularized these numbers

Originally these numbers came from India Egyptian Number System This language is composed of hieroglyphs, which are pictorial signs that represent numbers. 1 is shown by a single stroke.

10 is shown by a drawing of a hobble for cattle.

100 is represented by a coil of rope.

1,000 is a drawing of a lotus plant.

10,000 is represented by a finger.

100,000 by a tadpole or frog

1,000,000 is the figure of a god with arms raised above his head. Egyptian Hieroglyphs 10,000 100,000 1,000,000 Artifacts from over 30,000 years ago have distinctive tally marks on them.

It makes use of single strokes to represent object being counted.

30,000 years ago they tallied mainly animals.

One stroke is used for each object The introduction of grouping made it a lot easier to read numbers

We place a fifth tally mark across every four to make a group of 5 Today, this numeration system is used a lot in stastistics. How to count tallies The earliest example of tally marks was on the leg bone of a baboon found in Swaziland, dating to around 35,000 years ago. Name of Greek Number iota

pente

deka

hekaton

chilioi

myrioi The Number 1

5

10

100

1000

10000 The Greeks had two number systems. First is the Acrophonic or Herodian or Attic numerals. These numerals were used by the ancient Greeks. Second is the Milesian, Alexandrian, Ionic, or Alphabetic numerals. 1

5

9

10

50

90

100

500 Number Acrophonic Alphabetic These are Roman Numerals 1-10:

I, II, III, IV, V, VI, VII, VIII, IX, and X. Roman numerals remained in common use until about the 14th century where they were replaced it with Hindu-Arabic numerals Minuscule (lower case) letters were developed in the Middle Ages

ex: i, ii, iii, iv, vi, viii, viii, ix, and x. Modern Usage of Roman Numerals Names of monarchs and Popes, e.g. Elizabeth II of the United Kingdom, Benedict XVI. Page numbering of prefaces and introductions of books. Book volume and chapter numbers. Sequels of movies, video games.

The Olympic Games 50: L

100: C

500: D

1000: M Babylonion Numeral System Babylonian numerals were written in cuneiform, they used a wedge-tipped reed stylus to make a mark on a soft clay tablet which would be exposed in the sun to harden to create a permanent record. They used a sexagesimal (60 based) positional numeral system This system first appeared around 3100 B.C. It is also credited as being the first known positional numeral system Positional notation is a method of representing or encoding numbers. The positional numeral system is to be distinguished from other notations. * Only two symbols were used to count the 59 non-zero digits. These symbols and their values were combined to form a digit, similar to Roman Numerals. They had no symbol for zero, however if they really needed that zero they would just slant the symbol They seemed to like the number 60 because 60 is a very good number for a base. There are many factors to it (numbers which divide into it).

Factors of 60: 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 Babylonion number symbols This system originated in Mesopotamia How they combined their bigger numbers the number 424,000 represents decimal notation. Mayan Numeral System The Mayans had a number system that consisted of shells, dots, and lines.

You could write up to nineteen with just these symbols.

The Mayan's were one of the only ancient civilizations that understood the concept of zero. This allowed them to write very large numbers. This is part of a Mayan Calendar. This portion of this photo dates: 150 CE The Mayan system operated with place values. The 20 based Mayan numeral system Chinese Numeral System In 1899, a major discovery was made at an archaeological site of Xiao dun.

Thousands of bones and tortoise shells were discovered there, and they have been inscribed with ancient Chinese characters, mostly composed of chinese numerals.

The site had been the capital of the kings of the ancient Shang dynasty around 14th century BC The found artifacts showed many inscriptions of numerical information about men lost in battle, prisoners taken in battle, the number of sacrifices made, the number of animals killed on hunts, the number of days or months, etc. These were some of the symbols that were found in the inscriptions architects had discovered in Xiao dun Discovery of Chinese Numeral System The Chinese were the first to use a number system that used symbols based on a decimal system and that they used a positional value system. They had a 10 based system Traditional Chinese used rods from animal bones or bamboo

The Chinese system didn’t actually have a symbol for zero, but they were one of the first system to recognize the concept of zero. We see from the chart below that numbers 1 thru 9 could be arranged horizontally or vertically When writing numbers, the Chinese would alternate the vertical and horizontal arrangements so that the different number value places could be easily recognized Hindu- Arabic Numeral System Our modern day numbers

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# Ancient Number systems

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by Emily Pineda
on 10 June 2013
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