sumerian-math 𒁹 𒌋𒌋𒐉 𒐐𒁹 𒌋

Sumerian/Babylonian base-60 mathematics in pure JavaScript — no dependencies, ESM, works in Node 18+ and every modern browser.

Extracted from SumerianMath 3D, an interactive 3D scribe workshop.

Install

npm install sumerian-math

Usage

import {
  decimalToSexagesimalDigits,
  sexagesimalDigitsToDecimal,
  decimalToCuneiform,
  decimalToSexagesimalFraction,
  parseSexagesimalNotation,
  isRegularNumber,
  computeBabylonianSquareRoot,
  BABYLONIAN_RECIPROCALS,
} from 'sumerian-math';

// Integers ↔ base-60 places
decimalToSexagesimalDigits(405798);      // [1, 52, 43, 18]
sexagesimalDigitsToDecimal([2, 15]);     // 135

// Straight to cuneiform
decimalToCuneiform(75);                  // '𒁹 𒌋𒁹𒁹𒁹𒁹𒁹'  (1,15)

// Fractions and academic notation
decimalToSexagesimalFraction(Math.SQRT2, 3).notation;  // '1 ; 24, 51, 10'
parseSexagesimalNotation('1 ; 24, 51, 10');            // 1.4142129629629...

// Which divisors terminate in base 60?
isRegularNumber(54);  // true  (54 = 2·3³, so 1/54 terminates)
isRegularNumber(7);   // false (1/7 repeats forever, even for Babylonians)

// Division the Babylonian way: multiply by the reciprocal (IGI)
const igi8 = BABYLONIAN_RECIPROCALS.find(r => r.n === 8);
igi8.notation;        // '0 ; 7, 30'  (1/8 = 7/60 + 30/3600)

// Babylonian square root of 2 (the YBC 7289 value), starting from 1.5
computeBabylonianSquareRoot(2, 1.5, 3).at(-1).sexagesimal;  // '1 ; 24, 51, 10'

API

| Export | Description | |--------|-------------| | numberToWedges(n) | Splits a digit 0–59 into tens/ones with Unicode cuneiform and ASCII output | | decimalToSexagesimalDigits(n) | Integer → base-60 digit array, highest place first | | sexagesimalDigitsToDecimal(digits) | Base-60 digit array → integer | | decimalToCuneiform(n) | Integer → cuneiform string, places separated by spaces | | formatSexagesimal(digits) | Digit array → '2, 15' notation | | decimalToSexagesimalFraction(val, precision) | Float → a ; b, c, d notation with fractional places | | parseSexagesimalNotation(str) | '1 ; 24, 51, 10' → decimal float | | isRegularNumber(n) | True for 5-smooth numbers (terminating base-60 reciprocals) | | computeBabylonianSquareRoot(S, guess, steps) | Iteration trace of xₙ₊₁ = ½(xₙ + S/xₙ) | | BABYLONIAN_RECIPROCALS | The standard reciprocal (IGI) table of regular numbers | | CUNEIFORM_GLYPHS | Unicode cuneiform signs for digits and operations |

Notation

Sexagesimal places are separated by commas, and the fractional point by a semicolon, following standard Assyriological convention:

1;24,51,10 = 1 + 24/60 + 51/60² + 10/60³ ≈ 1.41421296

License

MIT