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Cistercian Numerals


Cistercian numerals are a family of decimal numeral systems that combine digit patterns around a common stem or stave. The basic notation represents the positive integers from 1 through 9999 by single compound symbols (King 2001, Miller 2020).

In one schematic vertical convention, the units occupy the upper right, tens the upper left, hundreds the lower right, and thousands the lower left (King 2001, p. 36). Thus the four compartments encode the decimal expansion

 n=1000a+100b+10c+d,

where a, b, c, and d are decimal digits, not all zero. A zero-valued position adds no stroke. This omission does not give a standalone numeral for zero in the basic notation (Miller 2020, p. 2).

An exact line segment realization of these vertical forms uses a stave from (0,-2) to (0,2) and points A=(0,2), B=(1,2), C=(0,1), and D=(1,1) in the units compartment. Its basic patterns for digits 1, 2, 3, 4, and 6 are the line segments AB, CD, AD, CB, and BD, respectively. The patterns for 5, 7, 8, and 9 combine those for 1 and 4, 1 and 6, 2 and 6, and 1, 2, and 6, respectively. The pattern for zero is empty. Reflection across the y-axis gives the tens patterns, while reflection across the x-axis gives the hundreds patterns. Both reflections give the thousands patterns. The four patterns and the common stave are combined into one symbol.

Each compartment has ten choices, an empty pattern or one of nine distinct nonempty patterns. Reading the compartments independently recovers the four digits, so this fixed convention gives exactly 10^4-1=9999 distinct nonzero numerals.

Historical forms vary in stave orientation, digit shapes, and place assignment. In particular, the triangular pattern for 5 used above is not universal (King 2001, pp. 34, 36, 39; Miller 2020).


See also

Decimal Expansion, Digit, Numeral, Numeral System

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References

King, D. A. The Ciphers of the Monks: A Forgotten Number-Notation of the Middle Ages. Stuttgart, Germany: Franz Steiner, 2001.Miller, K. "Background for Unicode Consideration of Cistercian Numerals." Dec. 10, 2020. https://www.unicode.org/L2/L2020/20290-cistercian-digits.pdf.Numberphile. "The Forgotten Number System." Featuring A. Bellos. Nov. 5, 2020. https://www.youtube.com/watch?v=9p55Qgt7Ciw.

Cite this as:

Weisstein, Eric W. "Cistercian Numerals." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CistercianNumerals.html

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