Evolution of Numerals

By Evan Evans

Some ancient numbers

Ancient numbers

Limits of Four

Visual Limits

• Humans have a visual distinguish “limit of four”.

• Different societies came up with ways to deal with this “limit of four”.

Egyptian 3rd Century BC

Cretan 1700-1200BC

England’s “five-barred gate”

Other Counting Methods

The Elema of New Guinea

Here is a figure to show you what some people have used

The Elema of

New Guinea

Counting Sticks

Additive Numeral Systems

• Some societies have an additive numeral system: a principle of addition

• Each character has a value independent of its position in its representation

• Greek and Roman numeral systems

The Greek Numeral System

Arithmetic with Greek Numeral System

Roman Numerals

1 I 20 XX2 II 25 XXV3 III 29 XIX4 IV (IIII) 50 L5 V 75

LXXV6 VI 100 C10 X 500 D11 XI 1000 M16 XVI

Now try these:

1. XXXVI 36

2. XL40

3. XVII 27

4. DCCLVI 756

5. MCMLXIX 1969

Roman Addition

MMMDCCCI

CCLXIV

+ DCL

+ MLXXX

+ MDCCCVII

264

+ 650

+ 1080

+ 1807 3801

Roman Subtraction

MMMDCCXXVIII

- MDCCCLII

- MCCXXXI

- CCCCXIIICCXXXII

3728

- 1852

- 1231

- 413232

Roman Multiplication

LXXV

x LMMMDCCL

75

x 503750

Chronograms

• “Time Writing”

• A sentence or Inscription in which the Capital or Highlighted Letters, interpreted in Roman Numerals, represent a particular date.

Chronogram

“My Day Is Closed In Immortality”

• a chronogram commemorating the death of Queen Elizabeth the first. 

M D I C I I

M D C I I I

1000+500+100+1+1+1

1603

Chronogram

Activity

Babylonian Maths

The Babylonians

Positional Notation

… Hundreds Tens Units

5 7 3

3600s 60s 1s

BabylonIan

sixties units =64 = 3604

Numbers Traveled

Through Exploration

Through Trade

Strong Arab Influence

From the Indian sub-continent to Europe via the Arabs

Roots of 1, 2, 3 and 4

In the WestThe Arabic numbers format are based traces with angles:

Number one (1) has one angle.

Number two (2) has two additives angles.

Number three (3) has three additives angles.

Number four (4) has four additive angles.

The number four get closed due to cursive hand write

Based Traced Angles

Which has Evolved into:

Roots of 5 through 10 numbers:

The circle is the symbol of the hand closed, which has five fingers.

The number five was written under the write line.

Joe has cows at home

Write Line

TEN

The number ten (the 2nd hand) was written (placed) on the top of  write line.

Theoretically, the circle on the top of the write line acquires double value (ten value).

Joe has Pigs at home

Additive Angles Theory

• For each number above 5 you add 1 angle

• Or for a number below 10 you subtract an angle

5 and 10

Additive Angles

5 5 + 1 5 + 1 + 1

6 75

Write line

Evolution of 5-6-7 in the West

Evolution of 8-9-10 in the West

Theory of 5-10

Evolution in Persia

The numbers evolved differently in Persia

Evolution in the East

In only 120 years the numbers had changed

The numerals from al-Sizji's treatise of 969

The numerals from al-Biruni's treatise copied in 1082

The Evolution of 2-3 in the East

• The numerals of 2 and 3 have been rotated 90 degrees

• Scribes copied text in columns from top to bottom onto scrolls

• Scribes unfamiliar with Indian numerals

Rotation of the numerals

Different dialects

Arabic-Indic ٨ ٧ ٦ ٥ ٤ ٣ ٢ ١ ٠ ٩

Eastern Arabic-Indic

(Persian and Urdu) ۰ ۱ ۲ ۳ ۴ ۵ ۶ ۷ ۸ ۹

Questions to Ask Yourselves

• Is this the end of our number system?

• Are there going to be any more changes in our present numbers?

• In 300 years from now, will the numbers have changed again to be something else?

Evolution of Numerals