Cyfry innych systemów pisma

Almost every numeral system on this page is older than the one you type with. The Western digits descend from the Brahmi numerals of India, which appear in Ashoka's rock edicts around 250 BCE. Brahmi was not positional: it carried separate signs for each unit, each multiple of ten and each hundred, so there was nothing for a zero to do. The decisive step came later, when Indian mathematicians began writing numbers as a string of nine digits with a dot or circle holding an empty column. MacTutor puts the earliest undisputed example at the Gwalior inscription of 876 CE; a legal document dated 594 CE is earlier, but historians suspect its date was added afterwards.

From India the system travelled west through Baghdad. Al-Khwarizmi (c. 780 – c. 850), a scholar at the House of Wisdom, wrote a treatise on calculating with Hindu numerals around 825. The Arabic original is lost and survives only in a Latin translation, Algoritmi de numero Indorum — and the Latinised form of his name became the word algorithm. Al-Kindi followed with his own account around 830. Europe took longer: the Codex Vigilanus of 976 shows the digits one to nine, without zero, in a Spanish monastery, and Gerbert of Aurillac, later Pope Sylvester II, had studied Arab science in Catalonia in the late 960s. Then in 1202 Leonardo of Pisa opened Liber Abaci by teaching merchants the modus Indorum.

Resistance was practical rather than superstitious. In 1299 the statutes of Florence's money-changers' guild, the Arte del Cambio, required members to write ledger entries out in words instead of abacus figures: an unfamiliar glyph is easy to alter, and a 0 becomes a 6 with one stroke of a pen. The popular story that medieval Europe outlawed zero as satanic is a modern invention. Positional notation won anyway, because ten signs serve every magnitude and the arithmetic can be done in columns on paper rather than on a counting board.

China met the same forgery problem and answered it differently. Under Wu Zetian, who reigned from 690 to 705, a second set of numerals came into use — 壹 貳 參 rather than 一 二 三 — chosen precisely because they are too intricate to pad with extra strokes. Banks in China still require them on cheques.

Najważniejsze właściwości

• The sixteen digit scripts here are positional base-ten systems and nothing more than a one-to-one substitution for 0–9, so they can write a number of any length.
• Unicode places each Indic script’s digits at a fixed offset inside that script’s own block — Devanagari zero at U+0966, Bengali zero at U+09E6, Tamil zero at U+0BE6 — which makes conversion pure arithmetic on code points.
• Standard subtractive Roman numerals reach only 3,999 (MMMCMXCIX), and the system has no symbol for zero; larger values need the vinculum or apostrophus conventions.
• Greek Ionic numerals keep three letters that had dropped out of the living alphabet: stigma for 6, koppa for 90 and sampi for 900. A keraia (U+0374) marks the 1–999 part and a lower keraia (U+0375) before a letter multiplies it by a thousand.
• Hebrew writes 15 as ט״ו and 16 as ט״ז instead of י״ה and י״ו, because those two spellings are forms of the divine name.
• Chinese financial numerals carry exactly the same values as the everyday ones but take many more strokes, so a figure in a ledger cannot be turned into a larger one by adding strokes to it.
• Japanese and Korean leave interior zeros unwritten — 1,000,001 is 百万一 in Japanese — while Chinese inserts 零 to mark the gap: 一百万零一.
• Babylonian arithmetic was base 60 and positional, built from just two signs, and had no zero; from about 300 BCE scribes used a placeholder in middle positions only, never at the end of a figure.

Gdzie się pojawiają

• Arabic-Indic digits are the everyday numerals on price tags, number plates and newspapers in Egypt, Sudan and the Arabian Peninsula, while the Maghreb mostly uses the Western forms.
• Thai digits are still printed on Thai banknotes and in official documents, usually beside the Western ones rather than instead of them.
• Chinese financial numerals are required on cheques, bank drafts and contracts; Japan prescribes its own equivalents (壱, 弐, 参, 拾) for legal and financial documents.
• Roman numerals survive on clock faces, in film copyright lines, on monument inscriptions and for regnal and papal names. American football numbered its championship games this way too, with one deliberate exception for Super Bowl 50.
• Hebrew numerals date the Jewish calendar year and number chapters and verses in printed Hebrew bibles.
• Gematria and numerology read meaning into the numeric value of words and names. That is a traditional interpretive practice with a long history, not an established result about numbers.