Alutor language facts for kids

Kids Encyclopedia Facts

Have you ever wondered how people counted before we had numbers like 1, 2, 3? Long ago, different cultures around the world came up with their own special ways to count and write down numbers. These systems helped them keep track of things, trade goods, and even understand time. Let's explore some of these amazing numeral systems from history and different types of counting methods!

Numbers Through Time and Cultures
How Numbers Are Written: Different Notations
History of Numeral Systems
Images for kids
See Also

Numbers Through Time and Cultures

People have been using numbers for a very long time. Different cultures developed their own ways to count, often based on how many fingers and toes they had! Here's a look at some of these systems and when they first appeared.

Name

Base (How many unique symbols are used before repeating)

Sample (What the numbers looked like)

Approx. First Appearance

Alutor Numerals

35,000 BCE

Babylonian numerals

3,100 BCE

Egyptian numerals

3,000 BCE

Chinese numerals, Japanese numerals, Korean numerals (Sino-Korean), Vietnamese numerals (Sino-Vietnamese)

零一二三四五六七八九十百千萬億 (Default, Traditional Chinese)

〇一二三四五六七八九十百千万亿 (Default, Simplified Chinese)

零壹貳參肆伍陸柒捌玖拾佰仟萬億 (Financial, T. Chinese)

零壹贰叁肆伍陆柒捌玖拾佰仟萬億 (Financial, S. Chinese)

1,600 BCE

Aegean numerals

𐄇 𐄈 𐄉 𐄊 𐄋 𐄌 𐄍 𐄎 𐄏 (

)
𐄐 𐄑 𐄒 𐄓 𐄔 𐄕 𐄖 𐄗 𐄘 (

)
𐄙 𐄚 𐄛 𐄜 𐄝 𐄞 𐄟 𐄠 𐄡 (

)
𐄢 𐄣 𐄤 𐄥 𐄦 𐄧 𐄨 𐄩 𐄪 (

)
𐄫 𐄬 𐄭 𐄮 𐄯 𐄰 𐄱 𐄲 𐄳 (

)

1,500 BCE

Roman numerals

I V X L C D M

1,000 BCE

Hebrew numerals

א ב ג ד ה ו ז ח ט
י כ ל מ נ ס ע פ צ
ק ר ש ת ך ם ן ף ץ

800 BCE

Indian numerals

Tamil ௦ ௧ ௨ ௩ ௪ ௫ ௬ ௭ ௮ ௯

Devanagari ० १ २ ३ ४ ५ ६ ७ ८ ९ Tibetan ༠ ༡ ༢ ༣ ༤ ༥ ༦ ༧ ༨ ༩

750 – 690 BCE

Greek numerals

ō α β γ δ ε ϝ ζ η θ ι
ο Αʹ Βʹ Γʹ Δʹ Εʹ Ϛʹ Ζʹ Ηʹ Θʹ

<400 BCE

Phoenician numerals

𐤙 𐤘 𐤗 𐤛𐤛𐤛 𐤛𐤛𐤚 𐤛𐤛𐤖 𐤛𐤛 𐤛𐤚 𐤛𐤖 𐤛 𐤚 𐤖

<250 BCE

Chinese rod numerals

𝍠 𝍡 𝍢 𝍣 𝍤 𝍥 𝍦 𝍧 𝍨 𝍩

1st Century

Ge'ez numerals

፩, ፪, ፫, ፬, ፭, ፮, ፯, ፰, ፱
፲, ፳, ፴, ፵, ፶, ፷, ፸, ፹, ፺, ፻

3rd – 4th Century, 15th Century (Modern Style)

Armenian numerals

Ա Բ Գ Դ Ե Զ Է Ը Թ Ժ

Early 5th Century

Khmer numerals

០ ១ ២ ៣ ៤ ៥ ៦ ៧ ៨ ៩

Early 7th Century

Thai numerals

๐ ๑ ๒ ๓ ๔ ๕ ๖ ๗ ๘ ๙

7th Century

Abjad numerals

غ ظ ض ذ خ ث ت ش ر ق ص ف ع س ن م ل ك ي ط ح ز و هـ د ج ب ا

<8th Century

Eastern Arabic numerals

٩ ٨ ٧ ٦ ٥ ٤ ٣ ٢ ١ ٠

8th Century

Western Arabic numerals

0 1 2 3 4 5 6 7 8 9

9th Century

Cyrillic numerals

А҃ В҃ Г҃ Д҃ Е҃ Ѕ҃ З҃ И҃ Ѳ҃ І҃ ...

10th Century

Tangut numerals

𘈩𗍫𘕕𗥃𗏁𗤁𗒹𘉋𗢭𗰗

1036

Burmese numerals

၀ ၁ ၂ ၃ ၄ ၅ ၆ ၇ ၈ ၉

11th Century

Maya numerals

<15th Century

Muisca numerals

<15th Century

Aztec numerals

16th Century

Sinhala numerals

෦ ෧ ෨ ෩ ෪ ෫ ෬ ෭ ෮ ෯

𑇡 𑇢 𑇣 𑇤 𑇥 𑇦 𑇧 𑇨 𑇩 𑇪 𑇫 𑇬 𑇭 𑇮 𑇯 𑇰 𑇱 𑇲 𑇳 𑇴

<18th Century

Kaktovik Inupiaq numerals

1994

How Numbers Are Written: Different Notations

Numbers can be written in many ways. Some systems use the position of a digit to show its value, like in our decimal system. Others use symbols that always mean the same amount, no matter where they are.

Standard Positional Numeral Systems

In these systems, the position of a digit changes its value. For example, in the number 123, the '1' means one hundred, the '2' means twenty, and the '3' means three. Our everyday number system is a positional system with a base of 10.

A binary clock uses lights to show numbers in binary. Each column of lights shows a number in a special code for time.

The names for these number bases often come from a mix of Latin and Greek words.

Base (Number of unique digits)	Name	Usage (Where it's used)
2	Binary	Used in digital computing (computers use 0s and 1s!). Also in some old measurement systems.
3	Ternary	Used in some math concepts and for counting prayer beads in Islam.
4	Quaternary	Used in data transfer and for describing DNA bases.
5	Quinary	Used in some languages for counting. Think of tally marks where you group by fives.
6	Senary	Used in some languages and for making random passwords (like Diceware).
7	Septenary	Used for timekeeping, like the days in a week.
8	Octal	Used in computer science, like for Unix-like permissions.
9	Nonary	A way to write ternary numbers more compactly.
10	Decimal / Denary	This is the most common system we use every day!
11	Undecimal	Used for check digits in ISBNs. Some cultures in New Zealand and Tanzania used a base-11 system.
12	Duodecimal	Used in some languages for counting. Think of a dozen (12) or a gross (144). Also used for 12-hour clocks and months.
13	Tridecimal	Used in some special math functions.
14	Tetradecimal	Used in some older calculators and for image processing.
15	Pentadecimal	Used in some languages and for routing phone calls over the internet.
16	Hexadecimal	Very important in computer science for showing binary data in a shorter way.
17	Heptadecimal	A less common base.
18	Octodecimal	Another less common base.
19	Enneadecimal	Another less common base.
20	Vigesimal	Used in many languages, like Basque and Maya. The Maya used a base-20 system.
21	Unvigesimal	A less common base.
22	Duovigesimal	A less common base.
23	Trivigesimal	Used in some languages like Kalam language.
24	Tetravigesimal	Used for 24-hour clock timekeeping.
25	Pentavigesimal	A less common base.
26	Hexavigesimal	Sometimes used for codes or ciphers, using all letters of the alphabet.
27	Heptavigesimal Septemvigesimal	Used in some languages. Can be used to create codes from letters.
28	Octovigesimal	Used for months timekeeping.
29	Enneavigesimal	A less common base.
30	Trigesimal	This base is special because it makes fractions like 1/2, 1/3, 1/5, and 1/6 end nicely.
31	Untrigesimal	A less common base.
32	Duotrigesimal	Used in Base32 encoding for computers.
33	Tritrigesimal	Used in some vehicle registration plates of Hong Kong.
34	Tetratrigesimal	Uses numbers and most letters.
35	Pentatrigesimal	Uses numbers and most letters.
36	Hexatrigesimal	Used in Base36 encoding, combining letters and digits.
37	Heptatrigesimal	Uses numbers and all letters of the Spanish alphabet.
38	Octotrigesimal	Uses all 12-base digits and all letters.
40	Quadragesimal	Used in older Digital Equipment Corporation computers for file names.
42	Duoquadragesimal	A less common base.
45	Pentaquadragesimal	A less common base.
48	Octoquadragesimal	A less common base.
49	Enneaquadragesimal	A compact way to write septenary numbers.
50	Quinquagesimal	Used in some older IBM computers for file names.
52	Duoquinquagesimal	A version of Base62 without vowels, or Base26 using both uppercase and lowercase letters.
54	Tetraquinquagesimal	A less common base.
56	Hexaquinquagesimal	A version of Base58.
57	Heptaquinquagesimal	A version of Base62 that excludes certain letters and numbers.
58	Octoquinquagesimal	Base58 encoding, used in things like Bitcoin addresses. It leaves out confusing characters.
60	Sexagesimal	The ancient Babylonian numerals used this base. We still use it for degrees (360 in a circle) and for hours, minutes, and seconds.
62	Duosexagesimal	Base62 encoding, using 0-9, A-Z, and a-z.
64	Tetrasexagesimal	Base64 encoding, very common for encoding data on the internet. It uses numbers, uppercase and lowercase letters, and two special characters.
72	Duoseptuagesimal	A less common base.
80	Octogesimal	A less common base.
81	Unoctogesimal	Related to base 3 (81 = 3x3x3x3).
85	Pentoctogesimal	Ascii85 encoding, used for encoding data into printable characters.
90	Nonagesimal	Related to some advanced math problems.
91	Unnonagesimal	Base91 encoding, uses almost all standard computer characters.
92	Duononagesimal	Base92 encoding, uses almost all standard computer characters, avoiding confusing ones.
93	Trinonagesimal	Base93 encoding, uses most printable characters, reserving some for special uses.
94	Tetranonagesimal	Base94 encoding, uses all printable characters.
95	Pentanonagesimal	Base95 encoding, like Base94 but includes the space character.
96	Hexanonagesimal	Base96 encoding, uses all printable characters plus two extra digits.
100	Centesimal	This is like using two decimal digits (100 = 10x10).
120	Centevigesimal	A less common base.
121	Centeunvigesimal	Related to base 11 (121 = 11x11).
125	Centepentavigesimal	Related to base 5 (125 = 5x5x5).
128	Centeoctovigesimal	Used in computing (128 = 2x2x2x2x2x2x2).
144	Centetetraquadragesimal	Like using two duodecimal digits (144 = 12x12).
256	Duocentehexaquinquagesimal	Base256 encoding, used in computing (256 = 2x2x2x2x2x2x2x2).
360	Trecentosexagesimal	Used for degrees in a circle.

Non-Standard Positional Numeral Systems

These systems are a bit different from the usual ones. They might have special rules or use different kinds of numbers as their base.

Bijective Numeration

In these systems, every number has only one way to be written. There's no "zero" digit in the usual sense; instead, the digits represent numbers from 1 up to the base.

Base	Name	Usage
1	Unary (Bijective base-1)	Think of Tally marks, where you just add one mark for each item.
2	Bijective base-2	A special way to write binary numbers.
3	Bijective base-3	A special way to write ternary numbers.
4	Bijective base-4	A special way to write quaternary numbers.
5	Bijective base-5	A special way to write quinary numbers.
6	Bijective base-6	A special way to write senary numbers.
8	Bijective base-8	A special way to write octal numbers.
10	Bijective base-10	A special way to write decimal numbers.
12	Bijective base-12	A special way to write duodecimal numbers.
16	Bijective base-16	A special way to write hexadecimal numbers.
26	Bijective base-26	Used for numbering columns in spreadsheets (like A, B, C, AA, AB...).

Negative Bases

Imagine counting with negative numbers as your base! These systems use a "nega-" prefix in their names.

Base	Name	Usage
−2	Negabinary	A way to represent numbers using a negative base.
−3	Negaternary	A way to represent numbers using a negative base.
−4	Negaquaternary	A way to represent numbers using a negative base.
−5	Negaquinary	A way to represent numbers using a negative base.
−6	Negasenary	A way to represent numbers using a negative base.
−8	Negaoctal	A way to represent numbers using a negative base.
−10	Negadecimal	A way to represent numbers using a negative base.
−12	Negaduodecimal	A way to represent numbers using a negative base.
−16	Negahexadecimal	A way to represent numbers using a negative base.

Signed-Digit Representation

In these systems, digits can be positive or negative. This can sometimes make calculations easier.

Base	Name	Usage
2	Balanced binary (Non-adjacent form)	A special way to write binary numbers with positive and negative digits.
3	Balanced ternary	Used in some Ternary computers.
4	Balanced quaternary	A special way to write quaternary numbers with positive and negative digits.
5	Balanced quinary	A special way to write quinary numbers with positive and negative digits.
6	Balanced senary	A special way to write senary numbers with positive and negative digits.
7	Balanced septenary	A special way to write septenary numbers with positive and negative digits.
8	Balanced octal	A special way to write octal numbers with positive and negative digits.
9	Balanced nonary	A special way to write nonary numbers with positive and negative digits.
10	Balanced decimal	Explored by mathematicians like John Colson and Augustin Cauchy.
11	Balanced undecimal	A special way to write undecimal numbers with positive and negative digits.
12	Balanced duodecimal	A special way to write duodecimal numbers with positive and negative digits.

Complex Bases

These are very advanced number systems that use complex numbers as their base. They are used in higher-level mathematics.

Base	Name	Usage
2i	Quater-imaginary base	Related to base -4 and base 16.
$\sqrt{2}i$	Base $\sqrt{2}i$	Related to base -2 and base 4.
$\sqrt[4]{2}i$	Base $\sqrt[4]{2}i$	Related to base 2.
$2 \omega$	Base $2 \omega$	Related to base 8.
$\sqrt[3]{2} \omega$	Base $\sqrt[3]{2} \omega$	Related to base 2.
−1 ± i	Twindragon base	Used to create the Twindragon fractal shape.
1 ± i	Nega-Twindragon base	Related to base -4 and base 16.

Non-Integer Bases

These systems use a number that isn't a whole number as their base. This can lead to interesting ways of representing numbers.

Base	Name	Usage
$\frac{3}{2}$	Base $\frac{3}{2}$	A rational non-integer base.
$\frac{4}{3}$	Base $\frac{4}{3}$	Related to duodecimal.
$\frac{5}{2}$	Base $\frac{5}{2}$	Related to decimal.
$\sqrt{2}$	Base $\sqrt{2}$	Related to base 2.
$\sqrt{3}$	Base $\sqrt{3}$	Related to base 3.
$\sqrt[3]{2}$	Base $\sqrt[3]{2}$	A non-integer base.
$\sqrt[4]{2}$	Base $\sqrt[4]{2}$	A non-integer base.
$\sqrt[12]{2}$	Base $\sqrt[12]{2}$	Used in music scales.
$2\sqrt{2}$	Base $2\sqrt{2}$	A non-integer base.
$-\frac{3}{2}$	Base $-\frac{3}{2}$	A negative rational non-integer base.
$-\sqrt{2}$	Base $-\sqrt{2}$	A negative non-integer base, related to base 2.
$\sqrt{10}$	Base $\sqrt{10}$	Related to decimal.
$2\sqrt{3}$	Base $2\sqrt{3}$	Related to duodecimal.
φ	Golden ratio base	Used in some early data encoding.
ρ	Plastic number base	A special mathematical constant.
ψ	Supergolden ratio base	Another special mathematical constant.
$1+\sqrt{2}$	Silver ratio base	A special mathematical constant.
e	Base $e$	Has the lowest "radix economy," meaning it's very efficient.
π	Base $\pi$	Uses the mathematical constant Pi as its base.
$e^\pi$	Base $e^\pi$	A very specific mathematical base.

p-adic Numbers

These are special kinds of numbers used in advanced math, especially in number theory.

Base	Name	Usage
2	Dyadic number	A type of number used in advanced math.
3	Triadic number	A type of number used in advanced math.
4	Tetradic number	Similar to dyadic numbers.
5	Pentadic number	A type of number used in advanced math.
6	Hexadic number	A type of number used in advanced math.
7	Heptadic number	A type of number used in advanced math.
8	Octadic number	Similar to dyadic numbers.
9	Enneadic number	Similar to triadic numbers.
10	Decadic number	A type of number used in advanced math.
11	Hendecadic number	A type of number used in advanced math.
12	Dodecadic number	A type of number used in advanced math.

Mixed Radix Systems

In these systems, the "base" changes for each position. Think of how we tell time: 60 seconds make a minute, 60 minutes make an hour, but then 24 hours make a day! The bases are different for each unit.

Factorial number system {1, 2, 3, 4, 5, 6, ...}
Even double factorial number system {2, 4, 6, 8, 10, 12, ...}
Odd double factorial number system {1, 3, 5, 7, 9, 11, ...}
Primorial number system {2, 3, 5, 7, 11, 13, ...}
{60, 60, 24, 7} in timekeeping (seconds, minutes, hours, days in a week)
{60, 60, 24, 30 (or 31 or 28 or 29), 12} in timekeeping (seconds, minutes, hours, days in a month, months in a year)
(12, 20) traditional English money system (£sd)
(20, 18, 13) Maya timekeeping

Other Notations

Quote notation
Redundant binary representation
Hereditary base-n notation
Asymmetric numeral systems optimized for non-uniform probability distribution of symbols

Non-Positional Notation

In these systems, the value of a symbol doesn't change based on its position. For example, in Roman numerals, 'V' always means five, no matter where it is in the number. All the earliest known number systems, before the Babylonian numerals, were non-positional. The French Cistercian monks even made their own unique numeral system.

History of Numeral Systems

The way people counted and wrote numbers changed a lot over time. For example, after the Ryūkyū islands were taken over by Satsuma in 1609, they did a land survey to figure out taxes. The Ryūkyū government then set up a poll tax (a tax on each person) in 1640.

To help people understand their taxes, especially those who couldn't read, community leaders used special methods. They used warazan, which was a way of calculating and recording numbers using straw. This was similar to the Quipu used by the Incas. After calculating, the tax for each household was written on a wooden plate called itafuda or hansatsu.

Special symbols called Kaidā glyphs were used on these wooden plates. These symbols were like pictures that helped people understand the numbers. In the early 1800s, an official named Ōhama Seiki designed "perfect" symbols for these plates. An old story from Yonaguni island says that about nine generations ago, a person named Mase taught the Kaidā glyphs and warazan to everyone. This happened in the late 1600s.

These methods were so good that people could even check if the official tax announcements were correct! The poll tax was finally stopped in 1903. The Kaidā glyphs and warazan were used until schools became common and more people learned to read and write. Today, these old symbols are still used on Yonaguni and Taketomi islands for art and souvenirs, showing their artistic value.

Images for kids

A binary clock shows time using only 0s and 1s.
Muisca numerals were used by the Muisca people in ancient Colombia.
Kaktovik Inupiaq numerals were created in Alaska in 1994.